test of normality against generalized exponential power ... · comes from a normal distribution....
TRANSCRIPT
Test of normality against
generalized exponential power alternatives
Alain Desgagne
Departement de Mathematiques, Universite du Quebec a Montreal
Pierre Lafaye de Micheaux1
Departement de Mathematiques et Statistique, Universite de Montreal
and
Alexandre Leblanc
Department of Statistics, University of Manitoba
CRM-3314
Abstract
The family of symmetric generalized exponential power (GEP) densities offers a
wide range of tail behaviours, which may be exponential, polynomial and/or logarith-
mic. In this paper, a test of normality based on Rao’s score statistic and this family of
GEP alternatives is proposed. This test is tailored to detect departures from normality
in the tails of the distribution. The main interest of this approach is that it provides a
test with a large family of symmetric alternatives having non-normal tails. In addition,
the test’s statistic consists of a combination of three quantities that can be interpreted
as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed
test is shown to perform well in terms of power when compared to its competitors.
1Corresponding Author
Key words: Test of normality, Rao’s score test, generalized exponential power, sym-
metric distributions, tail behaviour.
1991 MS Classification: 62E20, 62E25, 62F03, 60F05.
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1 Introduction
An important issue, in applied statistics, is the validity of the normality assumptions that
are often required for the use of many popular methods of statistical analysis. Consequently,
the problem of testing that a sample has been drawn from some normal distribution with
unknown mean and variance is one of the most common problems of goodness-of-fit in
statistical practice. For this, many test procedures have been proposed in the literature.
These tests can be mainly divided into three groups.
In the first group, the observed sample distribution is compared to the normal distribution
using some measure of discrepancy. This can be done in different ways, one of which is
the computation of a distance between the empirical distribution function (EDF) and the
normal cumulative distribution function (CDF). To accomplish this task, different norms
have been used. The tests proposed by Cramer (1928), Kolmogorov (1933) and Anderson
& Darling (1954) are very famous examples of this. See also Zhang & Wu (2005). Another
approach consists of assessing the closeness between a nonparametric estimate of the density
(usually a histogram, or some kernel estimator) and the normal density function. Again,
different norms have been used for this. Pearson’s χ2 test could be put into this category.
See also Fan (1994) and Cao & Lugosi (2005). Other approaches have also been considered.
For instance, we would also include in this group the procedure due to Epps & Pulley (1983)
which is based on the empirical characteristic function.
Moment based tests form the second group. Tests based on skewness or Pearson’s kurtosis,
or a combination of both, naturally fall into this group. See, for example, the tests proposed
by D’Agostino & Pearson (1973), Bowman & Shenton (1975), Jarque & Bera (1987) and
D’Agostino et al. (1990). We would also include here the test based on the ratio of the mean
(absolute) deviation to the standard deviation due to Geary (1935) and the test based on
G-Kurtosis introduced by Bonett & Seier (2002).
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The third group is composed of regression and correlation tests. See, for example, Shapiro &
Wilk (1965), D’Agostino (1971), Filliben (1975), Gan & Koehler (1990) and Coin (2008). The
Shapiro-Wilk test is quite possibly the most well-known and popular test of normality. It has
also been recognized as the best available omnibus tests by different authors who compared
the power of different tests for many different alternatives. See Shapiro et al. (1968), Pearson
et al. (1977) and D’Agostino & Stephens (1986, Section 9.4). Many authors have worked
on extensions of the Shapiro-Wilk test, including Shapiro & Francia (1972), Royston (1989,
1992) and Rahman & Govindarajulu (1997). Most of the tests in this group use a test
statistic that can essentially be viewed as the squared correlation R2 obtained from a normal
probability plot, that is, from a regression of the inverse normal CDF of the EDF on the
observations. The key here, is that R2 is expected to be close to unity when the sample
comes from a normal distribution.
There are, however, many other tests of normality in the literature, all based on different
ideas and characterizations of the normal distribution. Among them, we mention the test
of the ratio of the range to the standard deviation due to David et al. (1954) and the tests
related to entropy and the Kullback-Leibler information due to Vasicek (1976), Arizono
& Ohta (1989) and Park (1999). See also Locke & Spurrier (1976), Spiegelhalter (1977),
Oja (1983), LaRiccia (1986), Mudholkar et al. (2002) and Gel et al. (2007). For a compre-
hensive review of goodness-of-fit tests in general and in the particular case of normality, we
refer the reader to D’Agostino & Stephens (1986) and Thode (2002). Finally, more recent
papers on testing for normality are Carota (2010), Drezner et al. (2010), Goia et al. (2010),
Han (2010), Noughabi (2010), Sadooghi-Alvandi & Rasekhi (2009), Zghoul (2010). See
also the comprehensive simulation studies by Thadewald & Buning (2007) and Romao et
al. (2010).
In this paper, a new test of normality is proposed. This test is designed to detect non-normal
tail behaviour by considering a large family of symmetric alternatives and hence, is directional
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in nature. The strategy we adopt here, similar to the one used by Neyman (1937) or later by
Mardia et al. (1991), consists of using Rao’s score test (also known as the Lagrange multiplier
test, cf. Rao, 1948) and the generalized exponential power (GEP) family of densities which
can exhibit a large range of tail behaviours (cf. Desgagne & Angers, 2005). Specifically,
we develop a test of normality with unknown location and scale based on Rao’s score by
taking this vast family of densities as an alternative. Note that in the simple case where
location and scale are considered known, our procedure is equivalent to a test of a simple
null hypothesis about the GEP parameters. The resulting test statistic can be seen as a
combination of three measures of tail behaviour coming together to form an original and
simple test statistic having an asymptotically χ2 distribution with three degrees of freedom
under the null hypothesis.
For the remainder of this paper, we proceed as follows. In Section 2, the family of GEP
densities is presented and adapted for the purpose of our test. In Section 3, Rao’s score test
on the family of modified GEP densities is used to obtain a test of normality with unkown
location and scale. In Section 4, a Monte-Carlo simulation study is conducted to compare
the power of the proposed test with the power of other known tests of normality over a wide
range of alternatives. Finally, we briefly conclude in Section 5.
2 Generalized exponential power densities
The family of generalized exponential power densities covers a large range of tail behaviours,
ranging from exponential, to polynomial and logarithmic. This family of distributions has
been considered in applications where tail behaviour is of special interest, such as Bayesian
robustness (see Desgagne & Angers, 2007), the characterization of tails of distributions using
p-credence (see Angers, 2000) and the selection of an importance function in Monte Carlo
simulations (see Desgagne & Angers, 2005). In Section 3, we will use this family of densities
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as an embedding family of alternatives to develop a test of normality. This strategy can be
adopted because the normal density is included in the family of GEP densities. This idea is
not new and dates back to Neyman (1937). The main interest in the present approach is to
provide a simple and powerful test against symmetric alternatives.
Desgagne & Angers (2005) have defined the GEP density as having the following general
form,
p(x; γ, δ, α, β, z0) ∝ e−δ|x|γ
|x|−α (log |x|)−β if |x| ≥ z0,
and equal to p(z0; γ, δ, α, β, z0) for |x| < z0. Notice that the constant p(z0; γ, δ, α, β, z0) is
selected to make the density continuous. The density is symmetric with respect to the origin
and defined on the real line. The parameter space is a subset of R5 with other specific
conditions on the parameters guaranteeing that the density is proper, positive, bounded and
unimodal. For more details, see Desgagne & Angers (2005).
The exponential term, which includes the parameters γ and δ, provides a large spectrum
of tail behaviours. The polynomial term, controlled by the parameter α, provides densities
with heavy tails. The logarithmic term, using the parameter β, provides densities with even
heavier tails, sometimes called super heavy tails. The parameter z0 has little impact on the
tails of the density.
Certain known distributions are special cases of the GEP density. If the parameters α, β and
z0 are set to 0, we get the exponential power density introduced by Box & Tiao (1962). In
addition, if the parameter γ is set to 2, the normal density is obtained, and if it is instead
set to 1, we get the Laplace density. Also, the right tail of the GEP density (for x ≥ z0)
corresponds to certain known distributions. For example, the Weibull density is obtained by
letting α = 1 − γ and β = z0 = 0. Setting γ = 1, β = z0 = 0 and imposing the constraint
α < 1 gives the gamma density. The generalized gamma, Rayleigh and Maxwell-Boltzmann
densities can be obtained similarly. If the exponential term is removed (when γ = δ = 0),
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the GEP density is considered as a heavy-tailed distribution, with polynomial and possibly
logarithmic terms. For example, if we set γ = δ = β = 0 and impose the constraint α > 1,
the Pareto density is obtained. If we instead set γ = δ = 0 and z0 = 1 and impose the
constraints α > 1 and β < 1, we get the log-gamma density, an exponential transformation
of the gamma distribution. Letting γ = δ = 0 and α = 1 and imposing the constraints β > 1
and z0 > 1 leads to the super heavy-tailed log-Pareto density, an exponential transformation
of the Pareto distribution. Finally, note that GEP densities can approximate many classical
densities quite well in the tails, suggesting that a test of normality against GEP alternatives
should fare well against many non-GEP alternatives.
We now introduce a modified version of the GEP density to be used as a family of alternatives
for our test. This is done by setting certain parameters to fixed values and by adding carefully
chosen constants. Our rationale for doing this is the following.
First, note that the normal density N(0, σ2) is a special case of the GEP density, as it is
defined above, when γ = 2, δ = 12σ2 , α = 0, β = 0, z0 = 0. This means that δ is a function
of the scale parameter when normality is assumed. This is not desirable as the alternative
family will be extended to a location-scale family in the next section, our test statistic
incorporating classical maximum likelihood estimates of the location and scale parameters
under normality. In this context, we fix δ to avoid an additional degenerate term when
considering the score statistic (see (3) in the next section) and its use for the composite case.
We chose to set δ = 12
to include the N(0, 1) as a special case.
Secondly, it can be seen that the impact of the parameter z0 is greatest around the origin since
it essentially determines the constant part of the density. Its impact on the tail behaviour,
and consequently, its usefulness for detecting light and/or heavy tails can be expected to be
limited. We thus here set z0 = 0.
Finally, to ensure that the density remains positive and bounded for any values of the
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parameters γ, α and β, the constants 1 and e are added respectively to the polynomial and
logarithmic terms. Note that these constants have limited impact on the tail behaviour of
the densities.
The modified family of densities that results can be written in the following way. We will
write X ∼ GEP(θ) when the density of X is given by
g(x;θ) = k(θ) e−12|x|θ1 (1 + |x|
)−θ2( log(e + |x|))−θ3 , (1)
for all x ∈ R, where θ = (θ1, θ2, θ3)T is the vector of parameters, k(θ) is the normalizing
constant and θ1 ∈ R+, θ2 ∈ R and θ3 ∈ R. Note that the normalizing constant is generally
not available in closed form, although it is in simple cases. Also, the conditions θ2 ≥ 1 if
θ1 = 0, and θ3 > 1 if both θ1 = 0 and θ2 = 1, must be satisfied for the density to be proper.
We denote the resulting parameter space by Θ. Finally, note that the standard normal
density corresponds to the special case where θ = (2, 0, 0)T , and that this point is located in
the interior of the parameter space.
3 The proposed test for normality
Let X1, . . . , Xn be independent and identically distributed random variables with density
f(x;θ, µ, σ) =1
σg((x− µ)/σ;θ
),
where µ ∈ R and σ > 0 are respectively the unknown location and scale parameters, and
g(x;θ) is defined as in (1). We will write X ∼ GEP(θ;µ, σ) when the density of X is given
by f(x;θ, µ, σ).
Our goal, here, is to carry out a test that the measurements of X come from some N(µ, σ2)
8
distribution (with µ and σ unspecified), considering GEP distributions as a family of alter-
natives or, equivalently, assuming that these measurements come from some GEP(θ;µ, σ)
distribution. In other words, we want to test
H0 : L(X) ∈ {N(µ, σ2);µ ∈ R, σ > 0} = {GEP(2, 0, 0;µ, σ);µ ∈ R, σ > 0},
against (2)
H1 : L(X) ∈ {GEP(θ;µ, σ);θ ∈ Θ/{(2, 0, 0)T}, µ ∈ R, σ > 0},
with Θ denoting the parameter space introduced in Section 2.
Different approaches could be used to achieve this. Maximum likelihood techniques obviously
come to mind, but the fact that the normalizing constant k(θ) in (1) is in general not
analytically tractable makes the use of these techniques difficult. We here propose to take
a different approach and make use of Rao’s score test, considering µ and σ as nuisance
parameters. If we define
d0(y) =∂
∂θlog g(y;θ)
∣∣∣θ=(2,0,0)T
,
it can be shown that
d0(y) =
0.18240929− 1
2y2 log |y|
0.53482230− log(1 + |y|)
0.20981558− log(
log(e +|y|))
. (3)
Then the score vector to be used for our test is defined, for given values of µ and σ, as
rn(µ, σ) =1
n
n∑i=1
d0(Yi), (4)
where Yi = (Xi− µ)/σ. Note that the three included constants ensure that each component
9
of the score vector has zero mean under normality. Note also that the first element of the
vector in (3) is not defined for Yi = 0. However, by convention, we set it to zero when Yi = 0
since limy→0(y2 log |y|) = 0. It is worth noting that rn(µ, σ) consists of three new measures
of tail thickness given by
r(1)n (µ, σ) = 0.18240929− 1
2n
n∑i=1
Y 2i log |Yi|,
r(2)n (µ, σ) = 0.53482230− 1
n
n∑i=1
log(1 + |Yi|),
r(3)n (µ, σ) = 0.20981558− 1
n
n∑i=1
log(
log(e +|Yi|)).
As pointed out by a referee, it would be interesting to study more specifically the behaviour
of the above quantities and compare them, for example, to Pearson’s sample kurtosis or to
G-Kurtosis (cf. Bonett & Seir, 2002) in how they assess thickness of the tails of specific
distributions.
Now, under the null hypothesis of normality, the results of Rao (1948) imply that
n1/2rn(µ, σ)D−→ N3(0,J0) and n rn(µ, σ)TJ−1
0 rn(µ, σ)D−→ χ2
3, (5)
where the information matrix J0 is defined as
J0 = E0
[d0(Y )d0(Y )T
],
where Y = (X − µ)/σ and the notation E0[·] indicates that the expectation is taken under
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the null hypothesis. It is not difficult to show that
J0 =
0.42423099 0.13285410 0.05401580
0.13285410 0.10080860 0.04056528
0.05401580 0.04056528 0.01632673
, (6)
doing the involved numerical calculations by using Monte-Carlo simulations or any appro-
priate numerical integration method.
However, note that the result in (5) has no practical utility since, µ and σ being unknown,
rn(µ, σ) cannot be computed from the observations at hand. To circumvent this, the strat-
egy we adopt is quite natural, and similar to the one adopted by Jarque & Bera (1987).
Essentially, we still rely on the score vector, but use the maximum likelihood estimators of
µ and σ under normality, respectively
Xn =1
n
n∑i=1
Xi and Sn =
√√√√ 1
n
n∑i=1
(Xi − Xn)2,
as surrogates for the unknown µ and σ. Hence, we simply propose to base the composite test
of normality on rn(Xn, Sn). However, the repercussions of this substitution have to be well
understood. The remainder of this section is devoted to obtaining the asymptotic behaviour
of rn(Xn, Sn) and of the resulting test statistic.
For this, we first establish the (asymptotic) link between rn(Xn, Sn) and rn(µ, σ) so as to
make use of the results given in (5) above. An advantage of using this approach is that it
explicitly describes the effect of using Xn and Sn in lieu of the unknown parameters when
computing the test statistic.
Proposition 1. When X ∼ N(µ, σ2), we have that
rn(Xn, Sn) = rn(µ, σ)− 1
2(1− Tn)v0 + oP
(n−
12
)13,
11
where
Tn =1
n
n∑i=1
(Xi − µσ
)2
,
and where 13 = (1, 1, 1)T and
v0 = −E0
[Y 2d0(Y )
]= (0.86481850, 0.38512925, 0.15594892)T . (7)
A proof of this result is given in the Appendix with the vector v0 requiring the use of
numerical integration to be calculated.
Based on the previous result, it is now possible to determine the asymptotic distribution of
rn(Xn, Sn) and to present the statistic to be used for the composite test of normality, denoted
hereafter by Rn. The presentation of a proof of Theorem 1 is delayed to the Appendix. This
is our main result.
Theorem 1. The modified score vector for the composite test of normality of the hypothe-
ses given in (2) is rn(Xn, Sn) where rn is defined as in (4). Furthermore, under the null
hypothesis,
n1/2rn(Xn, Sn)D−→ N3
(0,J0 −
1
2v0v
T0
),
where J0 is given in (6) and the vector v0 is given in (7). The proposed statistic to test the
composite hypothesis of normality is given by
Rn = n rn(Xn, Sn)T(J0 −
1
2v0v
T0
)−1
rn(Xn, Sn),
and, under the null hypothesis, we have that RnD−→ χ2
3.
Note that the test statistic is location and scale invariant. Note also that the asymptotic
12
covariance matrix of n1/2rn(Xn, Sn) is given by
J0 −1
2v0v
T0 =
0.0502754623 −0.0336793487 −0.0134179540
−0.0336793487 0.0266463308 0.0105350321
−0.0134179540 0.0105350321 0.00416669944
,
which is quite different from the asymptotic covariance matrix of n1/2rn(µ, σ) given in (6).
We next study the power of the resulting procedure through some simulations. Comparisons
are made with many other tests that are available in the literature.
4 Practical Considerations and Simulations
In this section, we first give a formula to compute quantiles and p-values for our test for finite
sample sizes. This is done since the convergence in distribution of the statistic Rn seems
very slow. Then, we compare the power of the proposed test for the composite hypothesis
of normality with selected tests for different symmetric alternatives.
In order to see if the distribution of Rn, for finite samples, can be approximated by the
Chi-square distribution with 3 degrees of freedom, we estimated the power of our test under
the null hypothesis of normality, using the Chi-square quantiles, and we observed that the
results were too far from the exact level, for different levels and sample sizes. We concluded
that the use of simulated quantiles, or of a formula that estimates these quantiles, would be
necessary in practice. To derive such a formula, we simulated quantiles of different orders for
different sample sizes and were able to find a simple formula to estimate all these quantiles.
Specifically, we proceeded as follows.
For each sample size n given in Table 1, we found the best regression of the quantiles of
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order α explained by a power of α, ranging from 0.01 to 0.50. That is, we found the values
of an, bn and cn that maximize the R2 of the regression
qα;n = an + bnαcn , (8)
where qα;n is the simulated quantile such that Pr[Rn > qα;n] ≈ α. Doing this, we found the fit
to be remarkably good, R2 values ranging from 0.9995 to 0.9999 for all the considered sample
sizes. The coefficients an and bn and the exponent cn are given in Table 1. For example, if
n = 50 and the chosen level of the test is α = 0.05, then the hypothesis of normality of the
observations should be rejected if
R50 > q0.05;50 = −8.805 + 9.650(0.05)−0.17 = 7.2534.
Furthermore, a formula for p-values between 0.01 and 0.50 can easily be obtained by invert-
ing (8). This leads to
p-value ≈(Rn − an
bn
)1/cn, (9)
where Rn is the observed value of the test statistic. For example, if we observed R50 = 6.02,
the approximate p-value of the test would be
p-value ≈(6.02− (−8.805)
9.650
)1/(−0.17)
= 0.08,
and the hypothesis of normality would not be rejected at a level of α = 0.05. In addition to
the excellent fit of the regressions to estimate the quantiles, we assessed the quality of the
fit by performing a study of the empirical power under the null of Rn based on 1,000,000
simulations and on quantiles calculated from (8) and from the coefficients given in Table 1.
The results given in Table 2 suggest that the level of the test is very accurate using the
formula.
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Next, we performed simulations to compare the power of our proposed test based on Rn
for the composite hypothesis of normality with selected tests for different symmetric al-
ternatives. We selected all the test-competitors considered in Romao et al. (2010), an ex-
tensive empirical power study of tests for normality. These tests are Kolmogorov-Smirnov
(K − S), Anderson-Darling (AD∗), the Zhang-Wu ZC and ZA tests, the Glenn-Leemis-Barr
test (PS), the D’Agostino-Pearson K2 test, the Jarque-Bera test (JB), the Doornik-Hansen
test (DH), the Gel-Gastwirth robust Jarque-Bera test (RJB), the Hosking L-moments
based test (TLmom), the Hosking test based on trimmed L-moments (T(1)Lmom, T
(2)Lmom and
T(3)Lmom), the Bontemps-Meddahi tests (BM3−4 and BM3−6), the Brys-Hubert-Struyf MC-LR
tests (TMC−LR), the Bonett-Seier test (Tw), the Brys-Hubert-Struyf-Bonett-Seier joint test
(TMC−LR − Tw), the Cabana-Cabana tests (TS,5 and TK,5), the Shapiro-Wilk test (W ), the
Shapiro-Francia test (WSF ), the Rahman-Govindarajulu modification of the Shapiro-Wilk
test (WRG), D’Agostino’s D test (Da), the Filliben correlation test (r), the Chen-Shapiro test
(CS), Zhang’s Q test, the del Barrio-Cuesta-Albertos-Matran-Rodrıguez-Rodrıguez quantile
correlation test (BCMR), the β23 Coin test, the Epps-Pulley test (TEP ), the Martinez-
Iglewicz test (In) and the Gel-Miao-Gastwirth test (RsJ). We refer the reader to Romao et
al. (2010) for details and references on these tests. We also added the test of Spiegelhal-
ter (1977) (S), which is also a directional test for symmetric alternatives.
Different symmetric alternatives have been chosen. We first studied 142 GEP alternatives to
cover a large spectrum of tail behaviours. They are listed in Tables 3 to 6. For each of the
following kurtosis β2 of 1.1, 1.5, 1.84, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 4, 4.5, 5, 6, 10, 20, 50,
we considered several GEP with different parameters θ1, θ2, θ3. For each kurtosis, we plotted
these GEP densities in Figures 1 to 3. It is interesting to see that for the same kurtosis, the
tail behaviour can vary significantly. The kurtosis have been chosen to cover the densities
from very short-tailed to very heavy-tailed, and the parameters have been chosen to cover
all the possible shapes for each given kurtosis. We think that this set of alternatives is very
comprehensive and will give us the best indication of the performance of the tests to detect
15
non-normality for symmetric alternatives.
We also studied 28 symmetric alternatives considered in Romao et al. (2010) and usually in
the empirical power studies of tests for normality. They are listed in Tables 7 to 10. We find
the Beta, Location Contaminated Normal (LoConN), Tukey, Johnson SB (JSB), Johnson
SU (JSU), Student, logistic and Laplace, with their kurtosis β2 ranging from 1.5 to infinity.
This set of alternatives is relatively limited when covering the full spectrum of tail behaviours,
but it is still interesting to observe the performance of our test against the usual chosen al-
ternative in empirical studies not using GEP densities. Note also that we reparametrized the
classical Johnson SU distribution JSU(γ, δ, ξ, λ) to obtain our JSU(ν, τ, µ, σ) distribution
by letting ν = −γ, τ = 1/δ, µ = ξ−λ√
exp(δ−2) sinh(γ/δ) and σ = λ/c. Doing so, the mean
and standard deviation of our JSU distribution is respectively µ and σ. See Jonhson (1949)
for further details.
Note that we have included, in these tables, results for the GEP (1,−1.1, 0) alternative.
Our reason for doing so is that the Student-t(10) density is virtually undistinguishable from
that GEP density. It is interesting to note that all tests perform the same for both of these
alternatives, that is, for the Student density and its approximation by a GEP density. Again,
this suggests that a test of normality against GEP alternatives should fare well against non-
GEP alternatives that can be approximated by a member of the GEP family of distributions.
In Tables 3 to 10, we report the empirical power (as measured by the proportion of simulated
samples for which the composite hypothesis of normality was rejected) under the considered
alternatives. For our simulation study, we generated 1,000,000 samples under each alternative
(except for the GEP alternatives for which we generated 100,000 samples) and for sample
sizes of n = 20, 50, 100 and 200 at a significance level of 5%. We also report three measures
of performance for each test in each simulation. First, we report the average power against
all alternatives. Then, for each alternative, we also consider for each test the difference of its
power with the best one among all the tests for this specific alternative. These differences
16
are labeled in the tables as “Deviation to the Best” and, for each test, we report its mean
and maximum. The highest the first measure, and the smallest the last two measures, the
best is the performance of a test. We also report the rank of each test among the 34 tests,
for each one of the three quality measures.
When GEP alternatives are considered, our test Rn has the best rank for the three measures
for n = 50, n = 100 and n = 200, except for n = 50 where its rank is 6th for the maximum
deviation to the best, see Tables 3 to 6. For n = 20, its rank is 6th for the average of the
powers and the mean of the deviation to the best and 10th for the maximum deviation to
the best. These results clearly suggest that the test based on Rn has the best performance
among the 34 tests against the GEP alternatives for n ≥ 50.
When the 28 usual alternatives are considered, our test Rn performs relatively well, see
Tables 7 to 10. For n = 20 and n = 50, its rank is 14th for the three measures, for n = 100,
its rank is 10th, and for n = 200, its rank is 2nd for the two first measures and 5th for
the third one. Is is more difficult to make some conclusions with this more limited set of
alternatives, but it seems that our test becomes better as n increases, ranking among the
bests for n = 200.
In summary, our simulations suggest that our test, specifically designed to detect non-
normality in the tails for symmetric densities, has the best results for symmetric alternatives.
The performance seems to improve with the sample size, but the dominance of the test is
already visible at n = 50.
5 Conclusion
We have proposed a new test of normality based on using Rao’s score test on a GEP family
of distributions which includes the normal as a special case. This test is tailored to detect
17
departures from normality in the tails of the distribution. Our goal was to provide a simple
and intuitive test of normality against symmetric alternatives with non-normal tails. We
have obtained a test which is the most powerful against GEP alternatives compared to the
best normality tests previously available.
Appendix : Proofs
We first state a lemma needed for the proof of Proposition 1.
Lemma 1. If X ∼ N(µ, σ2), the vector rn(µ, σ) defined by (4) satisfies
∂
∂µrn(µ, σ) = oP (1)13 and
∂
∂σrn(µ, σ) = σ−1v0 + oP (1)13.
Proof of Lemma 1.
In order to prove this result, we work from the fact that
rn(µ, σ) =1
n
n∑i=1
d0(Yi).
Note that we can write d0(y) = (d1(y), d2(y), d3(y))T and that the following properties hold:
(i) dj(y) is an even function,
(ii) dj(Y ) is almost everywhere differentiable, implying that d0(Y ) and rn(µ, σ) are differ-
entiable with probability 1,
(iii) E0
[dj(Y )
]= E0
[Y dj(Y )
]= 0,
(iv) E0
[Y 2|dj(Y )|
]<∞,
18
(v) E0
[|d′j(Y )|
]<∞,
(vi) E0
[|Y d′j(Y )|
]<∞,
where d′j(y) = ddydj(y), for j = 1, 2, 3. On the other hand, by the weak law of large numbers,
we have
∂
∂µrn(µ, σ) = E0
[∂
∂µd0(Y )
]+ oP (1)13
= E0
[∂
∂µ
(d0
(X − µσ
))]+ oP (1)13,
a similar result holding for the partial derivative with respect to σ. Note that properties (v)
and (vi) are used here to ensure the weak law of large numbers can be applied. In order to
calculate the last expectation, first note that
E0
[∂
∂µdj
(X − µσ
)]= −σ−1 E0
[d′j(Y )
].
Now, recall Stein’s famous Lemma which, in the case of the standard normal distribution,
reduces to
E0
[h′(Y )
]= E0
[Y h(Y )
],
whenever these expectations exist (cf. Stein, 1981). Using this result with properties (iii)
and (v) leads to
E0
[d′j(Y )
]= E0
[Y dj(Y )
]= 0,
for j = 1, 2, 3 so that the first result is proved. In the same way, it is easy to verify that
E0
[∂
∂σdj
(X − µσ
)]= −σ−1 E0
[Y d′j(Y )
].
Using Stein’s Lemma one more time with h(Y ) = Y dj(Y ) and h′(Y ) = dj(Y ) +Y d′j(Y ), and
19
using properties (iii), (iv) and (vi), we have
E0
[Y d′j(Y )
]= E0
[dj(Y ) + Y d′j(Y )
]= E0
[Y 2dj(Y )
],
for j = 1, 2, 3 so that the second result also holds. �
Proof of Proposition 1.
Under normality, it is well known that
Xn − µ = OP (n−1/2). (10)
As a result, it is easy to verify that
S2n − σ2 = −σ2
(1− 1
n
n∑i=1
Y 2i
)− (Xn − µ)2 = −σ2
(1− Tn
)+ oP (n−1/2),
so that, upon applying the δ-method, we get
Sn − σ =1
2σ(S2
n − σ2) + oP (n−1/2) = −σ2
(1− Tn
)+ oP (n−1/2). (11)
Note that 1−Tn = OP (n−1/2) by the CLT. Now, to obtain the wanted result, we use a Taylor
expansion in probability of rn(Xn, Sn) along with (10), (11) and Lemma 1. This leads to
rn(Xn, Sn) = rn(µ, σ) + (Xn − µ)∂
∂µrn(µ, σ) + (Sn − σ)
∂
∂σrn(µ, σ) + oP (n−
12 )13
= rn(µ, σ)− 1
2
(1− Tn
)v0 + oP (n−
12 )13.
To conclude, it is sufficient to evaluate the vector v0 numerically, where v0 is given in
equation (7). �
Proof of Theorem 1. First, note that a proof of this theorem could also be obtained
20
using general results on score tests exposed in Cox & Hinkley (1979).
Now, note that Proposition 1 allows us to write
n1/2rn(Xn, Sn) = n1/2MZn + oP (1)13, (12)
where Zn = 1n
∑ni=1Zi, and where the matrix M and random vectors Zi are defined as
M =(I3 ; −1
2v0
)and Zi =
d0(Yi)
1− Y 2i
,
and where d0(y) and v0 are defined respectively in (3) and (7).
On the other hand, under the null hypothesis, the central limit theorem implies that
n1/2ZnD−→ N4
0,
J0 v0
vT0 2
, (13)
since
E0
[(1− Y 2)d0(Y )
]= −E0
[Y 2d0(Y )
]= v0.
Finally, (12) and (13) together imply that
n1/2rn(Xn, Sn)D−→ N3
(0,J0 −
1
2v0v
T0
).
The convergence in distribution of Rn follows directly. �
21
Acknowledgements
This research of A. Desgagne, P. Lafaye de Micheaux and A. Leblanc was supported by
the Natural Sciences and Engineering Research Council of Canada. The authors are also
grateful for the good time spent together during their doctoral years, when this project
started following discussions at a student seminar in the Department de Mathematiques et
de Statistique of the Universite de Montreal.
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27
Table 1: Set of parameters an, bn, cn for the two formulas (8) and (9), for 0.01 ≤ p-value,α ≤ 0.50
n an bn cn n an bn cn
10 -90.771 91.196 -0.02 270 -15.022 15.936 -0.12
20 -21.640 22.203 -0.08 280 -14.979 15.906 -0.12
30 -12.320 13.022 -0.13 290 -16.889 17.774 -0.11
40 -10.463 11.218 -0.15 300 -16.848 17.744 -0.11
50 -8.805 9.650 -0.17 310 -16.820 17.725 -0.11
60 -8.957 9.807 -0.17 320 -16.778 17.692 -0.11
70 -9.072 9.928 -0.17 330 -19.069 19.940 -0.10
80 -8.279 9.200 -0.18 340 -19.028 19.908 -0.10
90 -9.154 10.043 -0.17 350 -18.998 19.886 -0.10
100 -9.163 10.071 -0.17 360 -18.970 19.864 -0.10
110 -9.153 10.082 -0.17 370 -18.936 19.838 -0.10
120 -10.101 10.999 -0.16 380 -18.893 19.805 -0.10
130 -10.083 10.999 -0.16 390 -21.672 22.539 -0.09
140 -10.059 10.993 -0.16 400 -21.639 22.513 -0.09
150 -11.128 12.028 -0.15 410 -21.609 22.489 -0.09
160 -11.098 12.015 -0.15 420 -21.580 22.465 -0.09
170 -11.070 12.002 -0.15 430 -21.548 22.440 -0.09
180 -11.031 11.980 -0.15 440 -25.013 25.860 -0.08
190 -12.240 13.153 -0.14 450 -24.976 25.829 -0.08
200 -12.198 13.127 -0.14 460 -24.956 25.813 -0.08
210 -12.160 13.104 -0.14 470 -24.928 25.790 -0.08
220 -13.551 14.457 -0.13 480 -24.897 25.765 -0.08
230 -13.507 14.428 -0.13 490 -24.874 25.745 -0.08
240 -13.468 14.402 -0.13 500 -24.848 25.724 -0.08
250 -15.096 15.988 -0.12 1000 -54.342 55.166 -0.04
260 -15.058 15.963 -0.12 ∞ 64.056 -63.392 0.04
28
Table 2: Empirical power under the null of Rn based on 100,000 simulations and on quantilesgiven by formula in Table 1
n and α× 100 1 2 3 4 5 6 7 8 9 10 25 30 35 40 45 50
10 1.03 2.00 3.00 4.01 5.00 5.94 6.85 7.84 9.06 9.83 24.84 30.15 35.14 40.13 45.03 49.78
20 1.03 2.03 2.97 4.09 5.02 5.96 7.07 8.04 9.09 10.11 25.29 30.51 35.21 39.85 44.56 49.04
30 0.98 1.88 2.88 3.91 4.86 5.87 6.98 8.01 9.06 10.17 25.59 30.57 35.37 39.98 44.40 48.76
40 1.00 1.98 2.91 3.93 4.99 6.05 7.11 7.98 9.27 10.35 25.71 30.69 35.38 39.77 44.43 48.77
50 1.04 1.98 2.95 3.88 5.05 5.86 7.11 8.24 9.33 10.33 25.57 30.45 34.92 39.39 43.87 48.08
60 1.06 1.90 2.89 3.87 4.84 5.95 6.97 8.08 9.14 10.20 25.81 30.63 35.22 39.64 43.94 48.62
70 0.98 1.98 2.80 3.90 4.89 5.92 6.96 8.02 9.10 10.19 25.66 30.49 35.31 39.88 44.35 48.51
80 1.04 1.92 2.95 3.86 4.92 5.95 7.09 8.18 9.29 10.30 25.69 30.54 35.07 39.23 43.56 47.60
90 1.03 1.90 2.76 4.00 4.95 6.05 7.18 8.05 9.11 10.18 25.51 30.49 35.41 39.80 44.03 48.34
100 1.01 1.92 2.95 3.91 4.89 6.05 6.99 8.22 9.15 10.36 25.62 30.56 35.38 39.78 44.14 48.31
110 0.98 1.94 2.89 3.80 4.98 6.05 7.15 8.18 9.23 10.27 25.74 30.20 35.42 39.67 43.91 47.95
120 1.00 1.97 2.88 3.87 5.00 6.07 7.01 7.97 9.08 10.34 25.72 30.57 35.47 40.08 44.26 48.62
130 1.03 1.95 2.96 3.88 4.90 5.96 7.07 8.07 9.20 10.15 25.79 30.52 35.17 39.75 44.09 48.24
140 1.06 1.93 2.87 3.86 5.01 6.10 7.14 7.93 9.02 10.10 25.65 30.44 35.24 39.60 43.99 48.19
150 1.08 1.90 2.89 3.83 4.82 5.95 6.88 8.24 9.23 10.02 25.67 30.51 35.44 39.85 44.51 48.56
160 1.01 1.93 2.92 3.89 4.96 5.98 7.05 8.08 9.15 10.15 25.75 30.68 35.30 39.68 44.52 48.52
170 1.00 1.90 2.97 3.93 5.12 6.08 6.92 8.02 9.05 10.14 25.72 30.58 35.33 39.63 44.20 48.38
180 1.00 1.93 2.93 3.96 5.04 5.99 7.12 8.24 9.30 10.35 25.85 30.30 35.42 39.92 44.11 48.33
190 1.00 1.98 2.92 3.83 4.96 5.82 6.94 7.85 9.01 10.36 25.56 30.58 35.15 39.92 44.31 48.51
200 1.00 1.89 2.86 3.91 4.97 6.09 6.95 8.23 9.25 10.27 25.58 30.63 35.24 39.77 44.22 48.26
210 1.01 1.90 2.97 3.99 4.90 5.97 7.04 8.11 9.15 10.16 25.60 30.51 35.25 39.86 44.01 48.43
220 1.06 1.89 2.93 3.91 5.02 5.90 6.90 8.09 9.17 10.18 25.56 30.64 35.37 40.12 44.25 48.50
230 1.05 1.91 2.91 4.02 4.95 5.87 7.04 8.09 9.10 10.08 25.56 30.37 35.15 39.83 44.24 48.66
240 1.06 1.91 3.04 3.94 4.94 6.06 7.08 8.08 9.12 10.39 25.88 30.46 35.19 39.98 44.01 48.26
250 1.03 1.93 2.92 3.90 4.92 5.96 7.00 8.12 9.19 10.17 25.73 30.72 35.50 39.99 44.57 48.76
260 0.96 1.88 2.96 3.82 4.97 5.92 6.96 7.99 9.01 10.16 25.62 30.59 35.29 39.94 44.28 48.65
270 1.02 1.93 2.78 3.90 4.95 6.05 7.09 8.12 9.14 10.23 25.54 30.53 35.45 39.90 44.27 48.38
280 1.01 1.98 2.99 3.93 4.96 6.02 7.07 8.12 9.09 10.14 25.58 30.07 35.34 39.89 44.31 48.61
290 1.01 1.97 2.98 4.00 4.93 5.99 6.93 7.96 9.09 10.21 25.66 30.53 35.34 39.94 44.63 48.78
300 1.03 1.97 2.96 3.96 4.89 6.01 6.94 8.14 9.05 10.23 25.68 30.68 35.41 39.75 44.34 48.56
310 1.00 1.99 2.99 4.05 4.97 5.98 7.03 8.10 9.19 10.24 25.79 30.29 35.39 40.01 44.21 48.62
320 0.98 1.96 2.96 3.98 4.99 5.97 7.06 8.08 9.20 10.31 25.61 30.59 35.25 39.75 44.18 48.64
330 1.01 2.00 3.02 3.92 4.89 6.02 7.07 8.13 9.00 10.17 25.71 30.54 35.45 40.10 44.70 48.98
340 0.98 1.95 2.95 4.06 4.97 5.99 7.01 8.02 8.92 10.16 25.68 30.57 35.27 40.02 44.28 48.78
350 0.96 1.97 2.88 3.96 4.89 5.93 6.95 8.05 9.16 10.17 25.86 30.43 35.40 39.87 44.36 48.60
360 1.04 1.95 2.93 4.02 4.95 6.01 6.92 8.08 9.17 10.22 25.45 30.46 35.31 39.96 44.11 48.61
370 1.00 1.91 2.90 3.91 4.98 5.96 7.04 8.02 9.08 10.14 25.39 30.37 35.12 39.83 44.00 48.61
380 1.07 1.89 3.03 3.81 5.18 5.92 7.02 8.00 9.08 10.13 25.51 30.35 35.26 39.78 44.16 48.44
390 1.04 1.98 2.92 3.94 4.83 5.91 6.87 7.97 8.98 10.03 25.70 30.65 35.57 40.17 44.64 48.52
400 0.96 1.90 2.91 3.91 4.84 5.93 6.92 7.98 9.05 10.21 25.48 30.43 35.21 39.80 44.51 48.67
410 0.96 1.93 2.91 3.89 4.92 5.86 6.94 7.94 9.05 10.22 25.58 30.40 35.27 39.93 44.45 48.56
420 0.95 1.90 2.92 3.97 4.87 5.93 6.96 7.95 9.16 10.00 25.39 30.40 35.17 39.74 44.16 48.41
430 0.95 1.88 2.97 3.84 4.86 6.06 6.95 7.97 8.99 10.22 25.61 30.41 35.29 39.86 44.25 48.48
440 0.97 1.99 2.86 3.86 4.81 5.84 6.94 7.98 9.05 10.07 25.63 30.59 35.50 40.38 44.79 48.96
450 1.00 1.91 2.85 3.89 4.85 6.04 7.03 8.08 9.08 10.11 25.56 30.22 35.28 39.99 44.42 48.78
460 1.11 1.86 2.87 3.88 5.01 6.04 6.97 8.02 9.02 10.15 25.66 30.57 35.34 39.95 44.50 48.75
470 0.99 1.96 2.95 4.00 4.92 5.77 6.97 8.07 9.25 10.18 25.54 30.40 35.23 39.80 44.25 48.66
480 1.05 1.95 2.96 3.91 5.15 5.90 7.02 7.99 9.02 10.18 25.86 30.42 35.34 39.60 44.59 48.66
490 0.95 1.90 2.96 3.92 4.90 5.92 6.92 8.22 8.95 10.01 25.42 30.37 35.10 40.15 44.21 48.84
500 0.95 1.91 2.91 3.94 5.07 5.94 6.91 7.92 8.95 10.01 25.86 30.81 35.31 39.82 44.35 48.67
1000 0.94 1.92 2.86 3.87 4.85 6.11 6.96 8.05 9.10 10.04 25.44 30.23 35.13 39.77 44.59 48.60
29
Tab
le3:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=20
(beg
innin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
1.1
GE
P(1
,-40
.5,0
)10
010
010
010
010
089
.74.
210
04.
210
010
010
099
.74.
210
082
.596
.096
.68.
184
.810
010
010
034
.010
010
061
.110
090
.010
013
.954
.499
.894
.4
1.1
GE
P(4
,-18
.1,0
)10
010
010
010
010
089
.94.
110
04.
110
010
010
099
.44.
110
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99.9
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100
99.6
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3.9
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86.3
95.5
98.1
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84.4
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100
100
31.3
100
100
74.3
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94.5
100
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89.8
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GE
P(2
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74.2
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GE
P(4
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55.4
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26.2
67.2
63.4
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47.7
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63.2
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GE
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1.84
GE
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56.2
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GE
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1.84
GE
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GE
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GE
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GE
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GE
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27.
128
.138
.717
.84.
718
.923
.415
.430
.72.
513
.925
.48.
921
.711
.717
.73.
225
.113
.929
.5
2.5
GE
P(0
.7,-
3.9,
0)28
.426
.116
.011
.925
.79.
83.
28.
92.
512
.617
.718
.917
.33.
25.
723
.032
.513
.64.
315
.918
.411
.925
.32.
710
.820
.18.
116
.910
.214
.22.
922
.512
.023
.1
2.5
GE
P(0
.8,-
3.2,
0)22
.520
.713
.410
.020
.48.
32.
87.
42.
310
.814
.314
.713
.42.
84.
819
.227
.310
.74.
013
.615
.09.
521
.43.
18.
616
.57.
513
.79.
211
.82.
620
.010
.918
.3
2.5
GE
P(1
,-2.
7,0)
17.3
16.0
11.0
8.3
15.7
6.9
2.7
6.2
2.1
9.1
11.3
11.4
10.4
2.6
4.1
15.6
22.2
8.4
3.6
11.6
12.0
7.6
17.9
3.5
6.9
13.2
6.9
10.9
8.3
9.9
2.5
17.3
9.7
13.9
2.5
GE
P(1
.5,-
1.8,
0)9.
18.
87.
05.
48.
64.
52.
23.
81.
86.
06.
36.
05.
62.
23.
09.
612
.65.
32.
97.
67.
24.
511
.64.
94.
18.
05.
56.
46.
26.
42.
011
.37.
67.
7
2.5
GE
P(2
,-1,
0)6.
36.
35.
44.
36.
23.
41.
93.
21.
64.
64.
74.
74.
51.
92.
57.
68.
94.
62.
65.
65.
43.
59.
25.
13.
26.
04.
94.
95.
25.
21.
88.
46.
55.
9
2.5
GE
P(2
.8,0
,0)
4.7
4.6
4.1
3.3
4.5
2.6
1.6
2.4
1.5
3.7
3.9
4.4
4.4
1.6
2.1
6.0
6.3
4.4
2.2
4.3
4.1
2.7
7.1
5.1
2.5
4.5
4.0
3.7
4.4
4.0
1.7
6.4
5.7
5.0
2.5
GE
P(3
,0.2
,0)
4.7
4.4
3.7
3.0
4.3
2.4
1.6
2.3
1.4
3.4
4.0
4.4
4.4
1.6
2.0
5.9
5.8
4.3
2.0
4.0
3.8
2.4
6.7
5.1
2.3
4.1
3.9
3.3
4.2
3.8
1.7
5.8
5.5
4.8
2.5
GE
P(4
,0.9
,0)
4.2
4.0
3.3
2.7
3.9
2.1
1.5
2.1
1.5
3.1
4.3
4.9
5.0
1.5
1.9
5.2
4.9
4.4
1.9
3.4
3.4
2.4
6.0
4.8
2.3
3.7
3.5
3.1
4.0
3.5
1.8
4.9
5.4
4.9
2.5
GE
P(8
,1.9
,0)
4.2
3.8
2.7
2.2
3.7
1.6
1.2
1.9
1.5
2.7
5.7
6.8
6.6
1.2
1.8
4.8
3.9
4.6
1.6
2.5
2.9
2.2
4.9
4.5
2.1
3.0
2.8
2.7
3.6
3.1
2.1
3.9
5.1
5.4
2.5
GE
P(0
,730
,739
)22
.527
.324
.926
.027
.728
.330
.331
.335
.132
.420
.614
.210
.530
.132
.25.
727
.420
.526
.828
.125
.931
.415
.627
.931
.925
.017
.827
.730
.026
.327
.729
.128
.126
.0
2.75
GE
P(0
.5,-
5.3,
0)28
.625
.315
.912
.724
.99.
84.
49.
13.
511
.816
.818
.817
.94.
46.
423
.330
.012
.85.
514
.818
.112
.623
.43.
311
.819
.78.
417
.09.
113
.43.
820
.610
.523
.0
2.75
GE
P(0
.6,-
4.1,
0)25
.422
.214
.311
.521
.99.
04.
38.
33.
510
.815
.016
.715
.84.
36.
020
.926
.910
.95.
313
.516
.111
.321
.13.
410
.517
.68.
015
.18.
512
.13.
719
.29.
720
.3
2.75
GE
P(0
.7,-
3.3,
0)21
.518
.812
.610
.418
.58.
14.
27.
53.
39.
613
.014
.313
.34.
25.
518
.423
.49.
25.
112
.014
.010
.018
.63.
69.
315
.27.
613
.17.
810
.83.
617
.49.
017
.1
2.75
GE
P(0
.8,-
2.8,
0)17
.715
.511
.09.
115
.37.
34.
16.
63.
28.
710
.911
.811
.14.
15.
015
.719
.87.
64.
910
.711
.88.
516
.13.
87.
912
.97.
311
.17.
39.
43.
415
.68.
214
.0
2.75
GE
P(1
,-2.
3,0)
11.9
10.8
8.6
7.2
10.7
6.0
3.9
5.3
3.1
6.9
7.7
8.0
7.6
3.9
4.4
11.7
14.0
5.7
4.5
8.4
8.9
6.5
12.5
4.5
6.1
9.8
6.4
8.3
6.3
7.4
3.2
12.2
7.0
9.5
2.75
GE
P(1
.5,-
1.4,
0)6.
46.
15.
75.
06.
04.
43.
54.
02.
94.
84.
84.
74.
63.
53.
67.
37.
54.
53.
95.
65.
64.
47.
85.
04.
26.
05.
35.
34.
85.
13.
17.
35.
45.
6
2.75
GE
P(2
,-0.
5,0)
5.0
4.9
4.6
4.1
4.8
3.8
3.2
3.4
2.8
4.1
4.4
4.5
4.4
3.2
3.3
6.0
5.6
4.5
3.5
4.4
4.5
3.7
6.3
4.7
3.6
4.8
4.6
4.3
4.3
4.4
3.0
5.8
4.8
4.6
2.75
GE
P(2
.3,0
,0)
4.6
4.5
4.2
3.8
4.5
3.4
3.1
3.3
2.9
3.9
4.4
4.7
4.6
3.1
3.3
5.3
5.1
4.4
3.4
4.0
4.1
3.6
5.6
4.7
3.4
4.3
4.2
4.0
4.2
4.2
3.0
5.2
4.7
4.6
2.75
GE
P(3
,0.8
,0)
4.5
4.2
3.7
3.4
4.2
3.1
3.0
3.1
3.0
3.7
4.9
5.4
5.3
3.0
3.2
5.0
4.4
4.6
3.2
3.4
3.8
3.4
4.9
4.4
3.3
3.8
3.8
3.6
4.1
4.0
3.2
4.4
4.7
4.8
2.75
GE
P(4
,1.6
,0)
4.9
4.4
3.4
3.2
4.4
2.7
2.7
3.2
3.2
3.8
6.1
6.6
6.3
2.7
3.2
4.8
4.3
4.9
3.0
3.2
3.6
3.4
4.4
4.3
3.4
3.6
3.6
3.5
4.2
4.0
3.6
4.4
4.9
5.1
2.75
GE
P(0
,690
,706
)22
.327
.625
.026
.027
.928
.530
.531
.535
.332
.620
.614
.110
.530
.332
.35.
727
.520
.427
.128
.226
.031
.615
.728
.132
.125
.018
.027
.930
.026
.327
.829
.228
.325
.9
3G
EP
(0.5
,-4.
6,0)
23.5
20.1
13.9
11.8
19.9
9.3
5.8
8.6
4.7
10.2
13.5
15.5
15.1
5.8
6.7
19.7
23.2
9.6
6.5
12.5
15.2
11.8
18.8
4.1
11.2
16.4
8.4
14.5
7.9
11.2
4.5
17.0
8.6
18.8
3G
EP
(0.6
,-3.
6,0)
20.2
17.1
12.3
10.7
16.9
8.4
5.6
7.7
4.5
9.1
11.7
13.4
13.1
5.6
6.3
17.5
20.1
8.1
6.3
11.2
13.3
10.4
16.5
4.2
9.8
14.3
7.9
12.7
7.2
10.0
4.4
15.6
7.9
16.1
3G
EP
(0.7
,-2.
9,0)
16.7
14.3
11.1
9.8
14.1
7.8
5.7
7.1
4.5
8.2
10.0
11.0
11.0
5.6
6.0
15.1
17.0
6.8
6.2
10.1
11.6
9.3
14.3
4.5
8.8
12.5
7.7
11.2
6.7
8.9
4.3
13.8
7.1
13.4
3G
EP
(0.8
,-2.
5,0)
13.4
11.7
9.7
8.6
11.6
7.2
5.6
6.5
4.4
7.3
8.3
9.0
8.8
5.6
5.7
12.9
13.8
5.9
6.1
8.9
9.8
8.1
12.2
4.8
7.7
10.5
7.3
9.5
6.2
7.8
4.3
11.8
6.5
10.8
3G
EP
(1,-
1.9,
0)8.
88.
37.
87.
18.
26.
45.
55.
84.
56.
26.
06.
26.
05.
55.
49.
19.
55.
05.
77.
37.
66.
69.
15.
26.
48.
16.
67.
45.
66.
54.
48.
95.
77.
3
3G
EP
(1.5
,-1,
0)5.
45.
45.
75.
35.
35.
45.
25.
14.
64.
94.
54.
54.
45.
15.
05.
85.
74.
85.
15.
65.
45.
26.
15.
35.
15.
65.
45.
45.
05.
14.
65.
84.
95.
2
3G
EP
(2,0
,0)
5.1
5.1
5.2
4.9
5.1
5.1
5.1
5.1
5.0
5.0
5.1
5.1
5.0
5.1
5.2
5.0
5.1
4.9
5.1
5.0
5.0
5.2
5.2
5.2
5.1
5.0
5.1
5.0
5.2
5.0
5.0
5.2
5.1
5.2
30
Tab
le3:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=20
(con
tinuin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3G
EP
(3,1
.4,0
)5.
55.
44.
64.
55.
44.
64.
95.
15.
45.
56.
86.
96.
34.
85.
14.
65.
15.
44.
84.
54.
75.
14.
45.
15.
14.
64.
54.
85.
65.
15.
75.
25.
55.
8
3G
EP
(0,6
65,6
61)
22.3
27.5
25.1
26.1
27.8
28.7
30.7
31.3
35.4
32.6
20.6
14.2
10.5
30.4
32.5
5.7
27.4
20.6
27.1
28.2
26.1
31.6
15.7
28.2
32.1
25.1
17.8
28.0
30.0
26.3
27.8
29.1
28.2
26.0
3.5
GE
P(0
.5,-
3.8,
0)17
.114
.812
.711
.614
.710
.18.
79.
37.
29.
19.
411
.011
.38.
68.
515
.415
.56.
88.
711
.312
.911
.713
.76.
211
.413
.68.
912
.87.
59.
66.
612
.97.
014
.7
3.5
GE
P(0
.6,-
2.8,
0)14
.312
.611
.510
.812
.59.
68.
78.
97.
28.
48.
39.
49.
68.
68.
413
.312
.76.
08.
710
.211
.510
.811
.86.
410
.611
.98.
411
.56.
98.
76.
711
.26.
312
.4
3.5
GE
P(0
.7,-
2.3,
0)11
.410
.610
.610
.110
.69.
59.
08.
77.
48.
07.
07.
77.
88.
98.
410
.810
.55.
68.
89.
710
.310
.110
.26.
89.
910
.78.
210
.36.
98.
06.
99.
96.
210
.5
3.5
GE
P(0
.8,-
1.9,
0)9.
08.
99.
69.
28.
99.
18.
98.
67.
77.
66.
06.
26.
28.
88.
48.
98.
55.
48.
69.
09.
19.
48.
66.
99.
39.
37.
89.
37.
07.
67.
38.
55.
88.
7
3.5
GE
P(1
,-1.
4,0)
6.8
7.4
8.6
8.3
7.4
8.8
9.0
8.6
8.3
7.3
5.3
5.1
4.9
8.9
8.7
6.3
6.8
5.5
8.6
8.2
7.9
8.7
6.9
7.2
8.7
8.0
7.4
8.3
7.1
7.3
7.9
7.0
5.9
7.2
3.5
GE
P(1
.6,0
,0)
6.5
7.4
7.9
7.8
7.4
9.0
9.6
9.4
10.0
8.7
7.0
6.4
5.7
9.5
9.5
4.7
7.1
6.4
8.8
8.2
7.5
9.1
5.4
7.6
9.1
7.3
7.0
8.0
8.6
7.5
9.8
7.3
7.4
7.6
3.5
GE
P(2
,0.8
,0)
7.2
7.9
8.0
7.9
7.9
9.2
9.8
9.7
10.7
9.2
8.2
7.4
6.6
9.7
10.0
4.6
7.7
7.0
9.0
8.4
7.8
9.5
5.2
7.8
9.6
7.5
7.0
8.3
9.1
7.9
10.4
7.8
8.1
8.1
3.5
GE
P(3
,2.3
,0)
9.2
9.7
8.0
8.3
9.8
9.3
10.2
10.6
12.2
11.3
11.7
10.4
8.6
10.1
10.8
4.7
9.5
7.8
9.3
8.7
8.5
10.6
5.4
8.7
10.8
8.1
7.0
9.2
10.9
9.0
12.1
9.6
10.1
10.0
3.5
GE
P(0
,620
,609
)22
.227
.325
.126
.027
.728
.630
.631
.535
.232
.420
.414
.210
.430
.332
.45.
727
.320
.327
.128
.426
.131
.615
.728
.032
.025
.118
.127
.930
.226
.127
.729
.028
.125
.9
4G
EP
(0.4
,-4.
5,0)
16.4
14.7
14.0
13.4
14.7
12.2
11.4
11.4
9.7
10.1
8.9
10.4
10.7
11.4
10.9
14.3
13.5
6.7
11.2
12.4
13.9
13.7
13.1
8.2
13.5
14.4
10.0
14.1
8.4
10.3
8.6
12.1
7.2
15.3
4G
EP
(0.5
,-3.
2,0)
14.1
13.1
13.1
12.6
13.1
12.0
11.6
11.5
10.0
9.7
7.9
8.9
9.2
11.6
11.1
12.4
11.7
6.2
11.2
11.8
12.8
13.1
11.6
8.4
13.0
13.1
9.6
13.1
8.4
9.9
9.0
11.0
7.0
13.4
4G
EP
(0.6
,-2.
3,0)
11.6
11.6
12.6
12.2
11.5
12.1
12.0
11.6
10.5
9.7
6.8
7.4
7.7
11.9
11.4
10.3
10.1
6.2
11.4
11.6
12.0
12.8
10.3
8.9
12.7
12.2
9.8
12.4
8.6
9.5
9.5
10.1
7.0
12.0
4G
EP
(0.7
,-1.
9,0)
9.5
10.1
11.7
11.5
10.1
12.0
12.3
11.6
11.0
9.4
6.0
6.2
6.2
12.3
11.6
8.3
8.6
6.1
11.5
11.2
11.1
12.1
8.9
9.1
12.1
11.1
9.4
11.5
8.8
9.3
10.1
8.9
6.9
10.2
4G
EP
(0.8
,-1.
5,0)
8.1
9.4
11.4
11.2
9.4
12.2
12.7
11.9
11.8
9.9
5.8
5.4
5.1
12.6
12.1
6.6
8.2
6.4
11.9
11.2
10.5
12.0
7.9
9.5
12.1
10.4
9.3
11.1
9.4
9.3
10.9
8.6
7.5
9.4
4G
EP
(1,-
1.1,
0)7.
79.
311
.111
.09.
312
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45.
34.
913
.212
.95.
58.
67.
312
.111
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.37.
310
.012
.410
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211
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712
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98.
59.
3
4G
EP
(1.4
,0,0
)9.
311
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47.
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710
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111
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712
.112
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.314
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.111
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4G
EP
(2,1
.5,0
)11
.212
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315
.115
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713
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212
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.69.
713
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.416
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4G
EP
(3,3
.1,0
)13
.715
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.018
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.316
.217
.85.
115
.511
.414
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.613
.617
.57.
814
.517
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.314
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.118
.716
.216
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.2
4G
EP
(0,5
80,5
84)
22.4
27.5
25.2
26.1
27.9
28.6
30.6
31.7
35.4
32.8
20.8
14.2
10.5
30.4
32.5
5.9
27.6
20.6
27.1
28.4
26.1
31.7
15.7
28.3
32.1
25.2
18.2
28.0
30.3
26.4
28.1
29.3
28.3
26.2
4.5
GE
P(0
.4,-
4,0)
14.6
14.1
14.7
14.5
14.1
14.1
14.1
13.6
12.4
11.1
7.8
8.8
9.2
14.0
13.4
12.2
12.0
6.9
13.3
13.5
14.3
15.1
11.9
10.4
15.1
14.5
10.9
14.8
9.9
11.2
10.9
11.6
7.9
15.0
4.5
GE
P(0
.5,-
2.7,
0)12
.513
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57.
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013
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.18.
214
.0
4.5
GE
P(0
.6,-
2,0)
10.8
12.3
14.3
14.1
12.3
15.0
15.5
14.7
14.1
11.8
6.5
6.5
6.5
15.4
14.7
8.6
10.0
7.3
14.3
13.9
13.4
15.1
10.2
11.6
15.2
13.4
11.0
14.1
11.1
11.4
12.7
10.4
8.6
12.8
4.5
GE
P(0
.7,-
1.5,
0)9.
511
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65.
416
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810
.28.
114
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312
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.113
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.111
.713
.710
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611
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4.5
GE
P(0
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211
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15.
75.
216
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610
.88.
815
.314
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812
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.112
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.314
.113
.312
.315
.111
.310
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.8
4.5
GE
P(1
,-0.
8,0)
10.0
12.8
14.2
14.3
12.9
16.6
17.7
17.3
18.5
15.5
8.9
6.7
5.7
17.6
17.8
5.0
12.3
9.9
15.8
15.5
13.6
16.7
8.5
13.9
16.9
13.2
11.2
14.6
15.1
13.2
16.6
12.8
12.7
12.7
4.5
GE
P(1
.3,0
,0)
12.4
15.2
15.0
15.4
15.4
17.7
19.1
19.2
21.2
18.6
12.4
9.5
7.6
18.9
19.6
4.7
15.0
11.5
17.0
16.8
14.9
18.7
8.9
15.7
19.0
14.4
11.9
16.2
17.7
15.0
19.0
15.7
15.6
14.6
4.5
GE
P(2
,2.1
,0)
15.4
18.3
16.2
17.0
18.5
19.0
20.6
21.3
24.3
22.2
16.5
12.6
9.7
20.4
21.9
5.2
18.4
13.5
18.2
18.6
16.9
21.3
9.8
18.2
21.6
16.2
12.7
18.3
20.8
17.2
21.6
19.4
19.2
17.7
4.5
GE
P(3
,3.9
,0)
18.5
21.7
17.7
18.7
22.0
20.6
22.5
23.8
27.7
26.0
20.5
15.3
11.4
22.3
24.4
5.5
21.8
15.6
19.6
20.6
19.1
24.2
10.6
20.9
24.6
18.1
13.6
20.7
24.0
19.8
24.2
23.2
22.6
20.5
4.5
GE
P(0
,550
,557
)22
.427
.424
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.232
.620
.614
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.530
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.25.
727
.520
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.226
.031
.615
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.132
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.027
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.126
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.328
.326
.0
5G
EP
(0.5
,-2.
4,0)
12.1
13.9
15.9
15.9
13.9
16.8
17.5
16.8
16.3
13.6
7.0
6.9
7.0
17.4
16.8
9.1
11.5
8.3
16.1
15.8
15.1
17.2
11.0
13.2
17.3
15.0
12.2
15.9
12.7
12.8
14.2
12.1
10.0
14.9
5G
EP
(0.6
,-1.
7,0)
11.1
13.9
16.4
16.4
14.0
18.0
18.9
18.0
18.1
15.0
7.0
6.1
5.9
18.8
18.4
7.4
11.7
9.1
17.1
16.5
15.4
18.1
10.5
14.4
18.2
15.2
12.5
16.4
14.2
13.8
16.0
12.3
11.1
14.4
5G
EP
(0.7
,-1.
3,0)
10.8
14.2
16.4
16.5
14.3
18.6
19.7
19.1
19.7
16.4
7.7
5.9
5.2
19.6
19.4
6.0
12.8
10.3
17.8
17.4
15.6
18.6
10.2
15.5
18.8
15.2
12.8
16.6
15.8
14.5
17.4
13.5
12.8
14.2
5G
EP
(0.8
,-1,
0)11
.915
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46.
85.
720
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.05.
314
.411
.518
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.015
.014
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5G
EP
(1,-
0.6,
0)13
.617
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07.
122
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117
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.017
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.516
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5G
EP
(1.1
,0,0
)15
.519
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523
.024
.35.
219
.414
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.018
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.120
.223
.618
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.920
.322
.118
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.720
.620
.118
.7
5G
EP
(2,2
.7,0
)19
.623
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.420
.014
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.025
.727
.65.
623
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.422
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.112
.523
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.520
.715
.323
.326
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.025
.825
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.622
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5G
EP
(3,4
.6,0
)21
.926
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.223
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.331
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.127
.129
.85.
926
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.124
.025
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.726
.230
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.816
.125
.728
.924
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.928
.427
.324
.8
5G
EP
(0,5
00,6
00)
22.3
27.3
25.0
25.9
27.7
28.5
30.4
31.4
35.1
32.3
20.3
14.1
10.5
30.2
32.2
5.6
27.3
20.4
26.9
28.1
25.9
31.5
15.6
27.9
32.0
24.9
17.8
27.7
30.0
26.1
27.9
28.9
28.1
26.0
6G
EP
(0.4
,-2.
9,0)
14.1
17.0
19.4
19.4
17.1
21.0
21.9
21.1
21.0
17.4
7.9
7.1
7.1
21.8
21.3
9.1
13.9
10.4
20.1
19.6
18.5
21.4
12.9
17.0
21.6
18.3
14.3
19.5
16.5
16.1
17.8
14.7
13.0
18.0
6G
EP
(0.5
,-1.
9,0)
13.8
17.6
19.9
20.0
17.7
21.9
23.1
22.6
22.7
19.1
8.4
6.6
6.3
23.0
22.8
7.6
14.9
11.4
20.9
20.5
19.1
22.5
12.8
18.4
22.7
18.7
14.8
20.2
18.2
17.4
19.4
15.9
14.7
17.9
6G
EP
(0.6
,-1.
3,0)
14.1
18.6
20.7
20.9
18.7
23.4
24.8
24.4
25.2
21.6
9.5
6.7
5.7
24.6
24.8
6.2
17.1
13.4
22.3
22.1
20.0
23.8
12.8
20.1
24.1
19.5
15.6
21.4
20.7
19.0
21.3
17.8
17.3
18.5
6G
EP
(0.8
,-0.
8,0)
17.3
22.2
22.7
23.2
22.5
25.9
27.5
27.9
30.1
26.6
14.0
9.4
7.2
27.3
28.4
5.2
21.8
16.8
24.6
25.1
22.6
27.3
13.8
23.8
27.6
21.9
16.4
24.2
25.1
22.4
24.7
23.0
22.4
21.4
6G
EP
(1,0
,0)
22.2
27.3
24.9
25.9
27.7
28.5
30.4
31.2
35.0
32.2
20.5
14.2
10.4
30.2
32.0
5.6
27.3
20.3
26.8
28.1
25.8
31.4
15.6
28.0
31.8
24.9
18.0
27.6
30.0
26.0
27.5
29.1
28.1
25.9
6G
EP
(2,3
.9,0
)25
.731
.527
.428
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.616
.812
.033
.035
.76.
231
.423
.129
.231
.129
.235
.217
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.835
.728
.019
.431
.133
.729
.430
.333
.632
.329
.5
6G
EP
(3,6
.2,0
)27
.733
.528
.930
.533
.932
.434
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.439
.326
.317
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.834
.537
.66.
433
.424
.630
.632
.830
.937
.418
.533
.837
.929
.620
.533
.035
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.431
.435
.834
.231
.2
6G
EP
(0,1
40,1
29.1
)22
.828
.125
.626
.628
.429
.131
.132
.236
.033
.320
.814
.410
.630
.932
.95.
727
.921
.027
.528
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.632
.216
.128
.932
.725
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.229
.728
.726
.5
10G
EP
(0.4
,-1.
7,0)
24.5
31.4
32.0
32.9
31.7
35.6
37.5
37.8
39.9
35.8
15.3
9.0
6.8
37.3
38.6
7.0
29.6
23.1
33.7
34.9
32.0
37.5
21.3
33.6
37.8
31.2
22.3
33.9
33.8
31.5
29.6
31.2
30.2
30.2
10G
EP
(0.5
,-1,
0)28
.836
.334
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.036
.638
.440
.641
.444
.641
.620
.812
.08.
240
.442
.46.
235
.127
.536
.338
.135
.741
.523
.637
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.934
.623
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.638
.635
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.637
.235
.834
.0
10G
EP
(0.7
,0,0
)42
.249
.141
.744
.149
.744
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.449
.755
.954
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.825
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.547
.151
.28.
447
.837
.742
.245
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.151
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.948
.752
.543
.727
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.449
.545
.533
.451
.948
.645
.5
10G
EP
(1.4
,5.7
,0)
35.7
42.8
38.0
40.0
43.2
41.5
43.8
45.7
50.6
48.6
29.6
18.8
13.0
43.6
46.9
7.0
42.0
32.8
39.2
42.1
40.3
46.7
26.5
43.5
47.1
39.1
25.5
42.5
44.4
40.7
32.6
45.1
42.8
39.9
10G
EP
(0,6
,12.
2)32
.238
.834
.736
.239
.238
.340
.642
.246
.744
.427
.017
.612
.540
.443
.26.
638
.529
.936
.338
.736
.542
.923
.939
.543
.335
.323
.938
.640
.936
.831
.541
.239
.336
.5
10G
EP
(0,1
7,-1
2.6)
32.7
39.2
35.2
36.8
39.6
38.9
41.1
42.6
47.2
44.9
27.2
17.5
12.2
40.9
43.7
6.7
38.8
30.2
36.6
39.2
37.1
43.2
24.2
40.1
43.7
35.9
23.8
39.2
41.3
37.4
31.9
41.5
39.6
36.8
20G
EP
(0.3
,-1.
3,0)
45.0
52.8
48.1
50.1
53.2
51.2
53.8
55.6
60.0
58.2
32.9
18.2
11.3
53.5
57.0
8.2
51.2
42.2
48.5
52.2
50.4
56.7
35.9
53.8
57.2
49.2
32.0
52.6
53.8
50.8
33.2
54.6
51.9
49.3
20G
EP
(0.5
,0,0
)64
.771
.159
.963
.671
.561
.064
.067
.274
.474
.958
.241
.228
.563
.769
.114
.467
.157
.557
.763
.665
.471
.748
.869
.472
.163
.938
.867
.568
.065
.329
.173
.567
.865
.9
20G
EP
(0.8
,2.3
,0)
54.1
61.6
53.8
56.5
62.0
56.2
58.9
61.3
67.1
66.6
44.7
28.2
18.5
58.6
62.9
10.0
59.3
49.5
53.1
57.7
57.6
63.9
42.0
61.3
64.4
56.1
35.2
59.7
60.8
58.0
31.9
64.1
60.0
57.1
20G
EP
(0,1
4,-1
7.6)
43.3
50.8
45.2
47.5
51.3
48.4
50.9
52.8
57.9
56.4
34.6
21.6
14.5
50.7
54.2
8.0
49.7
40.5
45.6
49.5
48.0
54.3
33.5
51.4
54.8
46.7
30.2
50.1
51.7
48.3
32.5
53.3
50.4
47.7
20G
EP
(0,6
,2.6
)39
.847
.142
.044
.047
.545
.447
.749
.554
.452
.532
.020
.213
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.550
.87.
546
.236
.843
.046
.144
.450
.730
.547
.651
.243
.128
.346
.548
.344
.932
.449
.447
.044
.1
50G
EP
(0.3
,-0.
7,0)
70.9
77.0
67.4
70.7
77.3
68.0
70.7
73.6
79.9
80.2
61.1
40.9
26.2
70.4
75.4
15.2
73.1
64.7
64.5
70.4
72.3
77.5
57.2
75.7
77.9
71.0
43.8
74.1
73.9
72.3
25.4
78.9
73.8
72.1
50G
EP
(0.4
,0,0
)81
.685
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.878
.686
.173
.776
.479
.586
.687
.675
.759
.042
.776
.281
.523
.780
.173
.670
.076
.780
.785
.066
.483
.885
.379
.448
.482
.281
.079
.719
.487
.380
.781
.1
50G
EP
(0.6
,1.2
,0)
76.9
82.3
72.6
76.1
82.6
72.4
75.1
78.0
84.0
84.9
67.8
47.4
31.3
74.9
79.8
18.0
77.5
70.1
68.8
74.9
77.6
82.3
63.3
80.9
82.7
76.4
47.1
79.3
78.5
77.5
22.1
83.8
78.0
77.4
50G
EP
(0,5
.1,2
.1)
44.1
51.4
45.8
48.0
51.8
49.0
51.4
53.4
58.3
56.9
35.1
21.9
14.6
51.1
54.6
8.1
50.3
41.2
46.4
50.0
48.5
54.7
34.3
51.9
55.2
47.2
30.3
50.6
52.4
48.9
32.2
53.9
51.1
48.1
50G
EP
(0,8
,-7.
2)50
.958
.251
.754
.158
.654
.657
.059
.164
.463
.440
.124
.716
.156
.860
.69.
356
.447
.151
.655
.754
.861
.140
.158
.461
.653
.633
.956
.858
.155
.331
.660
.457
.154
.3
50G
EP
(0,1
0,-1
3.8)
57.0
64.1
56.8
59.5
64.5
59.2
61.7
64.1
69.4
68.8
45.6
28.1
18.1
61.4
65.5
10.5
61.9
52.7
56.0
60.8
60.5
66.3
45.4
64.0
66.8
59.1
37.2
62.5
63.4
60.8
30.3
66.3
62.5
60.0
50G
EP
(0,1
0.8,
-17.
3)62
.769
.561
.364
.470
.063
.065
.768
.274
.173
.951
.432
.720
.765
.469
.811
.966
.657
.559
.764
.865
.571
.250
.169
.171
.764
.139
.867
.567
.965
.728
.771
.767
.265
.1
Mea
n
2027
.530
.827
.625
.230
.824
.815
.426
.216
.728
.623
.119
.316
.315
.324
.017
.231
.922
.714
.827
.428
.426
.728
.316
.926
.228
.917
.128
.326
.926
.412
.226
.927
.928
.5
Ran
k
2012
2.5
1120
2.5
2131
18.5
295
2325
3032
2226
124
3313
716
8.5
2818
.54
278.
514
.517
3414
.510
6
Dev
.to
the
Bes
t-
Mea
n
209.
05.
78.
911
.35.
711
.721
.110
.319
.77.
813
.417
.220
.221
.212
.419
.24.
613
.821
.79.
18.
19.
88.
219
.610
.37.
619
.48.
29.
510
.124
.39.
68.
68.
0
Ran
k
2012
2.5
1120
2.5
2131
18.5
295
2325
3032
2226
124
3313
716
8.5
2818
.54
278.
514
1734
1510
6
Dev
.to
the
Bes
t-
Max
2048
.923
.225
.839
.423
.642
.096
.040
.796
.335
.152
.268
.175
.396
.155
.666
.922
.450
.391
.928
.920
.942
.126
.192
.946
.517
.873
.324
.144
.434
.191
.745
.839
.231
.9
Ran
k
2021
47
145
1632
1534
1223
2628
3324
253
2230
92
178
3120
127
618
1129
1913
10
31
Tab
le4:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=50
(beg
innin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
1.1
GE
P(1
,-40
.5,0
)10
010
010
010
010
037
.110
010
01.
310
010
010
010
010
010
089
.610
010
014
.099
.510
010
010
097
.610
010
090
.310
010
010
010
.183
.310
010
0
1.1
GE
P(4
,-18
.1,0
)10
010
010
010
010
037
.010
010
01.
210
010
010
010
010
010
090
.310
010
018
.099
.510
010
010
092
.410
010
094
.410
010
010
09.
686
.010
010
0
1.1
GE
P(6
,-14
.6,0
)10
010
010
010
010
037
.110
010
01.
110
010
010
010
010
010
091
.310
010
021
.799
.410
010
010
089
.210
010
095
.510
010
010
09.
586
.710
010
0
1.1
GE
P(8
,-12
.9,0
)10
010
010
010
010
037
.610
010
01.
110
010
010
010
010
010
092
.110
010
025
.299
.410
010
010
087
.310
010
096
.410
010
010
09.
587
.210
010
0
1.1
GE
P(1
5,-1
0.9,
0)10
010
010
010
010
038
.110
010
01.
010
010
010
010
010
010
094
.110
010
032
.099
.310
010
010
084
.410
010
097
.510
010
010
09.
488
.010
010
0
1.1
GE
P(3
0,-1
0,0)
100
100
100
100
100
38.7
100
100
1.0
100
100
100
100
100
100
95.9
100
100
36.0
99.3
100
100
100
83.8
100
100
98.2
100
100
100
9.2
88.5
100
100
1.1
GE
P(6
0,-9
.8,0
)10
010
010
010
010
038
.910
010
01.
010
010
010
010
010
010
096
.710
010
037
.099
.310
010
010
083
.910
010
098
.510
010
010
09.
188
.710
010
0
1.5
GE
P(1
,-8.
3,0)
100
100
99.9
99.7
100
98.8
50.7
97.5
0.3
99.9
100
100
100
55.2
98.9
86.3
99.6
100
14.9
97.4
100
100
100
1.0
100
100
39.1
100
95.8
100
0.5
86.2
80.5
99.1
1.5
GE
P(2
,-5.
7,0)
99.9
100
99.8
99.3
100
99.4
43.7
98.4
0.2
99.9
100
99.9
99.7
48.9
99.3
75.7
99.5
99.9
17.0
97.6
100
99.8
100
0.5
99.7
100
44.9
99.9
98.0
100
0.3
88.8
87.8
98.8
1.5
GE
P(4
,-3.
7,0)
97.3
99.9
99.7
99.3
99.9
99.7
37.3
98.9
0.1
99.9
99.3
97.4
93.1
42.7
99.3
62.9
99.4
99.2
17.3
97.7
99.8
98.8
100
2.8
98.4
99.9
56.8
99.7
99.4
99.8
0.2
91.8
96.1
98.4
1.5
GE
P(6
,-2.
9,0)
93.8
99.6
99.8
99.5
99.7
99.7
35.4
98.9
0.1
99.9
98.1
92.0
82.4
40.6
99.1
60.2
99.2
98.2
16.7
97.7
99.7
98.4
100
6.8
97.7
99.9
65.8
99.6
99.7
99.7
0.1
92.9
98.6
97.9
1.5
GE
P(8
,-2.
5,0)
91.5
99.4
99.8
99.6
99.5
99.6
34.7
98.8
0.1
99.9
96.7
87.5
74.0
40.0
98.8
59.9
99.0
97.3
16.4
97.5
99.7
98.1
100
9.5
97.3
99.8
71.5
99.5
99.7
99.5
0.1
93.2
99.3
97.6
1.5
GE
P(1
5,-2
.1,0
)87
.499
.299
.999
.899
.399
.633
.398
.50.
199
.893
.878
.761
.338
.398
.559
.798
.695
.815
.797
.499
.898
.110
013
.097
.399
.980
.799
.699
.999
.20.
193
.799
.997
.1
1.5
GE
P(3
0,-1
.9,0
)85
.899
.299
.999
.999
.299
.633
.198
.40.
199
.892
.274
.455
.438
.398
.459
.698
.495
.215
.897
.299
.898
.310
013
.897
.699
.985
.599
.799
.999
.00.
193
.610
096
.8
1.5
GE
P(6
0,-1
.8,0
)85
.099
.299
.999
.999
.299
.633
.098
.40.
199
.891
.372
.453
.338
.098
.359
.398
.394
.715
.597
.199
.898
.410
014
.197
.799
.987
.299
.799
.999
.00.
193
.610
096
.5
1.84
GE
P(0
.6,-
8.4,
0)99
.899
.989
.284
.099
.978
.27.
065
.70.
390
.699
.099
.599
.68.
671
.678
.698
.099
.18.
079
.098
.095
.597
.10.
494
.598
.420
.197
.766
.993
.20.
480
.038
.496
.9
1.84
GE
P(0
.8,-
6,0)
99.3
99.8
86.6
80.6
99.8
77.8
5.5
63.5
0.3
89.8
98.4
99.1
99.0
6.9
69.5
73.8
97.8
98.6
7.5
78.0
96.6
92.5
96.0
0.3
91.1
97.2
20.1
96.0
67.1
91.9
0.3
80.6
38.4
96.4
1.84
GE
P(1
,-5,
0)97
.899
.383
.176
.499
.377
.14.
161
.50.
288
.597
.297
.997
.45.
267
.067
.097
.497
.66.
876
.994
.287
.994
.60.
585
.995
.419
.893
.267
.690
.10.
280
.938
.495
.5
1.84
GE
P(1
.5,-
3.9,
0)88
.094
.975
.367
.595
.276
.12.
256
.80.
285
.691
.490
.086
.32.
961
.249
.995
.891
.65.
774
.285
.873
.190
.03.
869
.788
.520
.583
.570
.084
.30.
181
.840
.390
.8
1.84
GE
P(2
,-3.
2,0)
75.4
87.7
70.1
62.2
88.2
75.4
1.4
52.9
0.1
82.9
83.0
77.3
69.4
1.9
56.4
38.8
93.4
83.0
4.6
72.2
78.4
61.3
86.5
11.3
57.3
82.3
21.6
75.1
72.3
78.9
0.1
81.6
42.9
83.9
1.84
GE
P(3
,-2.
1,0)
56.3
75.1
65.6
57.7
75.9
74.6
0.8
48.2
0.1
78.2
66.4
53.8
42.3
1.2
50.4
28.7
87.1
67.7
3.6
69.2
69.4
48.5
83.0
26.7
44.1
74.6
23.7
64.8
75.4
70.3
0.1
78.8
48.2
72.1
1.84
GE
P(4
,-1.
4,0)
44.7
66.5
64.2
56.6
67.4
73.7
0.6
45.1
0.0
74.2
53.9
38.5
27.5
0.8
46.2
24.0
80.7
57.2
3.1
66.6
65.0
41.8
81.9
38.0
37.4
70.8
26.0
59.6
77.5
64.3
0.0
74.8
53.3
64.7
1.84
GE
P(6
,-0.
7,0)
33.6
57.9
65.1
58.0
58.9
72.5
0.4
41.8
0.0
69.4
39.4
23.6
15.3
0.6
41.8
21.1
71.7
46.4
2.5
63.5
62.2
37.0
82.6
48.7
32.4
68.7
30.3
56.1
80.1
57.2
0.0
68.0
62.0
57.0
1.84
GE
P(8
,-0.
4,0)
29.3
54.1
67.0
60.3
55.0
72.0
0.4
40.6
0.0
67.1
32.8
18.2
11.4
0.5
39.9
19.7
66.8
41.5
2.3
62.2
62.3
35.9
84.0
52.5
31.4
68.9
33.9
55.7
81.7
53.8
0.0
64.1
68.3
53.5
1.84
GE
P(1
5.2,
0,0)
23.8
50.3
71.3
65.9
51.2
71.2
0.3
38.9
0.0
63.9
24.4
12.1
7.5
0.4
37.4
17.9
60.2
35.4
2.0
59.7
64.0
35.9
87.1
55.9
31.0
70.7
41.4
56.8
84.1
49.0
0.0
58.7
78.1
49.4
2G
EP
(0.5
,-8.
9,0)
99.0
99.4
77.5
70.9
99.5
64.2
3.7
49.3
0.6
79.8
96.7
98.5
98.7
4.5
54.6
74.2
96.0
97.1
6.7
65.5
93.2
87.6
91.4
0.7
85.7
94.3
16.5
92.4
52.1
83.1
0.5
76.0
26.9
95.3
2G
EP
(0.8
,-5.
1,0)
95.9
97.7
69.8
62.7
97.9
61.3
2.3
44.4
0.4
76.0
93.4
95.7
95.6
2.9
49.0
64.4
94.9
94.2
5.7
61.6
86.7
77.3
86.7
0.7
74.5
88.7
15.7
85.2
51.1
78.0
0.4
75.7
25.8
93.2
2G
EP
(1,-
4.2,
0)90
.494
.363
.456
.294
.559
.31.
540
.90.
373
.089
.091
.090
.02.
044
.755
.193
.590
.05.
059
.180
.067
.382
.31.
563
.982
.915
.377
.750
.973
.40.
375
.425
.590
.1
2G
EP
(1.5
,-3.
2,0)
68.3
78.3
50.7
43.8
79.1
54.7
0.7
33.0
0.2
65.3
73.2
70.9
65.5
1.0
35.2
35.5
87.3
72.4
3.6
52.5
62.4
44.8
71.6
8.5
41.0
67.0
15.1
58.6
50.9
61.2
0.2
73.4
25.4
75.1
2G
EP
(2,-
2.5,
0)50
.863
.444
.037
.764
.351
.70.
428
.30.
159
.157
.951
.243
.50.
629
.425
.979
.157
.22.
947
.851
.532
.665
.117
.629
.156
.915
.347
.051
.052
.30.
169
.026
.460
.5
2G
EP
(3,-
1.4,
0)31
.845
.738
.132
.546
.747
.80.
222
.80.
150
.337
.427
.720
.80.
322
.817
.964
.939
.21.
942
.140
.621
.859
.030
.718
.846
.416
.135
.651
.941
.10.
059
.728
.744
.1
2G
EP
(4,-
0.7,
0)23
.237
.036
.230
.737
.845
.50.
119
.90.
044
.826
.617
.412
.10.
219
.515
.254
.630
.61.
638
.536
.017
.657
.237
.714
.942
.117
.030
.952
.834
.80.
051
.831
.736
.7
2G
EP
(6,0
,0)
15.9
29.2
36.5
30.7
29.9
43.6
0.1
17.1
0.0
38.9
16.4
9.5
6.6
0.1
16.1
12.9
43.9
22.7
1.2
35.0
33.2
14.3
57.6
43.5
11.8
39.6
19.0
27.7
54.5
28.6
0.0
42.8
37.4
30.4
2G
EP
(8,0
.3,0
)13
.326
.437
.532
.027
.042
.60.
116
.00.
036
.012
.97.
25.
30.
114
.911
.638
.519
.41.
133
.332
.713
.559
.445
.011
.039
.421
.026
.955
.825
.70.
038
.042
.228
.0
2G
EP
(15,
0.7,
0)10
.623
.441
.335
.624
.141
.20.
014
.30.
032
.78.
85.
14.
30.
113
.010
.232
.415
.90.
830
.934
.013
.063
.545
.510
.541
.025
.027
.558
.122
.10.
032
.751
.025
.4
2G
EP
(0,8
65,8
73)
43.6
55.0
46.0
45.6
56.0
49.1
55.4
57.3
66.1
62.2
42.4
29.8
21.9
56.0
60.3
7.3
62.8
51.0
42.1
59.3
52.5
59.4
26.9
60.0
60.2
48.8
27.1
54.2
60.9
52.3
55.1
63.8
69.4
58.2
2.25
GE
P(0
.5,-
7.2,
0)93
.994
.955
.349
.795
.244
.12.
630
.01.
159
.087
.192
.994
.03.
032
.963
.689
.088
.06.
045
.077
.066
.874
.61.
264
.079
.412
.975
.333
.961
.51.
067
.315
.690
.8
2.25
GE
P(0
.7,-
4.7,
0)87
.489
.447
.542
.489
.940
.02.
125
.50.
953
.880
.587
.187
.92.
327
.555
.286
.281
.95.
240
.067
.455
.067
.81.
451
.870
.712
.165
.131
.754
.90.
865
.314
.386
.9
2.25
GE
P(0
.8,-
3.8,
0)78
.681
.641
.236
.682
.337
.11.
622
.30.
849
.773
.479
.579
.51.
923
.746
.282
.974
.04.
536
.658
.644
.861
.52.
241
.862
.411
.555
.730
.549
.10.
764
.013
.681
.2
2.25
GE
P(1
,-3.
3,0)
67.0
71.0
35.0
31.1
71.9
34.1
1.4
19.3
0.6
45.1
64.7
69.1
67.8
1.6
20.0
37.4
78.1
64.0
3.9
33.0
49.0
34.8
54.6
4.0
31.8
53.2
11.0
45.9
29.3
43.1
0.6
61.6
12.8
72.0
2.25
GE
P(1
.5,-
2.4,
0)36
.942
.023
.120
.542
.926
.60.
712
.60.
333
.739
.037
.333
.30.
812
.220
.558
.836
.72.
524
.129
.316
.840
.111
.914
.733
.79.
926
.026
.628
.90.
350
.411
.840
.9
2.25
GE
P(2
,-1.
7,0)
22.9
27.9
17.4
15.7
28.6
22.1
0.4
9.4
0.2
26.3
24.9
21.3
17.6
0.5
8.5
14.1
44.5
23.8
1.8
19.0
20.7
10.2
32.8
16.9
8.7
24.5
9.3
17.7
24.3
21.4
0.2
40.6
11.3
26.1
2.25
GE
P(3
,-0.
5,0)
11.9
16.0
13.3
11.7
16.5
17.3
0.2
6.3
0.1
18.4
12.3
9.1
7.1
0.2
5.3
9.8
28.0
13.8
1.2
13.9
13.8
5.6
27.2
21.0
4.6
17.2
8.7
11.2
22.3
14.2
0.1
27.2
11.4
15.5
2.25
GE
P(3
.7,0
,0)
9.2
13.1
12.4
10.8
13.5
15.9
0.1
5.3
0.1
15.7
9.0
6.6
5.4
0.2
4.4
8.6
22.6
11.2
1.0
12.2
12.3
4.5
25.7
21.7
3.6
15.5
8.7
9.7
21.5
12.0
0.1
22.5
11.7
13.2
2.25
GE
P(4
,0.2
,0)
8.1
11.8
12.0
10.4
12.2
15.3
0.1
4.9
0.1
14.5
7.7
5.8
4.9
0.1
4.0
8.3
20.6
10.2
1.0
11.6
11.5
4.1
25.2
22.1
3.3
14.7
8.4
9.1
21.2
11.1
0.1
20.5
12.0
12.1
2.25
GE
P(8
,1.2
,0)
5.0
7.6
11.3
9.3
7.8
12.0
0.0
3.1
0.1
9.3
4.1
4.6
5.1
0.1
2.4
6.2
11.3
6.5
0.6
8.3
9.4
2.7
25.6
21.2
2.1
12.4
8.9
7.0
20.5
7.1
0.0
11.9
15.1
9.9
2.25
GE
P(0
,785
,782
)43
.654
.846
.245
.755
.849
.555
.657
.666
.362
.342
.529
.721
.856
.260
.57.
363
.251
.442
.159
.652
.559
.726
.960
.160
.448
.927
.354
.461
.352
.155
.164
.169
.858
.5
2.5
GE
P(0
.5,-
6.1,
0)83
.483
.738
.435
.384
.329
.63.
719
.11.
940
.872
.282
.584
.93.
920
.253
.877
.273
.06.
329
.858
.047
.555
.92.
244
.761
.111
.556
.121
.841
.91.
956
.59.
284
.2
2.5
GE
P(0
.7,-
3.9,
0)70
.870
.830
.728
.371
.625
.53.
115
.41.
734
.960
.970
.873
.03.
415
.843
.270
.761
.05.
625
.045
.935
.046
.92.
632
.649
.210
.443
.619
.634
.61.
752
.58.
375
.3
2.5
GE
P(0
.8,-
3.2,
0)57
.056
.824
.622
.857
.821
.82.
712
.61.
529
.950
.257
.959
.02.
912
.533
.663
.148
.74.
920
.835
.825
.539
.23.
923
.539
.19.
733
.517
.828
.51.
548
.47.
562
.7
2.5
GE
P(1
,-2.
7,0)
43.0
42.9
19.5
18.3
43.8
18.6
2.3
10.2
1.3
25.3
39.3
44.1
43.6
2.5
9.7
25.0
53.4
36.2
4.3
17.2
27.1
17.9
32.3
5.6
16.3
30.2
8.9
24.8
16.3
23.0
1.2
42.8
6.9
46.5
2.5
GE
P(1
.5,-
1.8,
0)18
.318
.810
.810
.719
.311
.71.
55.
80.
915
.317
.517
.315
.51.
64.
912
.529
.615
.83.
010
.113
.27.
319
.99.
66.
415
.57.
211
.512
.412
.90.
826
.75.
417
.8
2.5
GE
P(2
,-1,
0)10
.311
.07.
67.
611
.48.
71.
04.
00.
710
.59.
78.
77.
61.
13.
28.
618
.79.
72.
26.
98.
64.
215
.310
.73.
610
.56.
27.
110
.68.
90.
617
.95.
19.
8
2.5
GE
P(2
.8,0
,0)
6.2
6.8
5.5
5.6
7.0
6.2
0.6
2.6
0.5
7.0
5.5
5.1
4.8
0.7
2.0
6.7
10.8
6.5
1.6
4.5
5.9
2.6
12.3
10.3
2.2
7.4
5.3
4.7
8.6
6.4
0.4
10.9
4.8
6.1
2.5
GE
P(3
,0.2
,0)
5.5
6.1
5.1
5.1
6.3
5.6
0.6
2.4
0.5
6.3
5.0
4.6
4.4
0.6
1.9
6.3
9.6
6.0
1.5
4.1
5.3
2.3
11.8
10.2
2.0
6.7
5.2
4.2
8.4
5.8
0.4
9.7
4.8
5.8
2.5
GE
P(4
,0.9
,0)
4.5
4.8
4.2
4.1
4.9
4.4
0.4
1.7
0.5
4.6
4.2
4.9
5.1
0.4
1.3
5.5
6.5
5.0
1.1
3.1
4.2
1.7
10.6
9.3
1.4
5.5
4.7
3.3
7.3
4.5
0.4
6.8
5.0
5.4
2.5
GE
P(8
,1.9
,0)
4.4
4.3
3.6
3.1
4.4
2.7
0.2
1.0
0.4
2.8
5.6
8.0
8.6
0.2
0.9
4.6
3.7
4.3
0.8
1.7
3.8
1.4
10.4
7.2
1.2
4.7
3.8
2.8
5.8
3.5
0.5
3.8
6.1
6.9
2.5
GE
P(0
,730
,739
)43
.654
.945
.745
.555
.848
.855
.057
.265
.962
.142
.829
.822
.155
.660
.27.
362
.851
.341
.759
.252
.459
.326
.859
.860
.248
.727
.154
.161
.052
.154
.863
.869
.458
.4
2.75
GE
P(0
.5,-
5.3,
0)70
.568
.328
.727
.269
.321
.55.
714
.33.
428
.356
.369
.373
.45.
914
.645
.363
.056
.37.
721
.143
.334
.841
.03.
632
.846
.010
.941
.614
.828
.53.
345
.55.
975
.9
2.75
GE
P(0
.6,-
4.1,
0)63
.360
.424
.923
.861
.519
.45.
412
.73.
225
.350
.062
.266
.05.
612
.840
.058
.449
.47.
219
.037
.329
.336
.23.
827
.539
.810
.335
.613
.625
.13.
242
.75.
370
.0
2.75
GE
P(0
.7,-
3.3,
0)53
.750
.221
.320
.451
.317
.45.
111
.23.
122
.342
.553
.056
.25.
311
.133
.752
.641
.16.
716
.730
.923
.631
.24.
122
.133
.49.
729
.312
.621
.63.
139
.34.
960
.8
2.75
GE
P(0
.8,-
2.8,
0)43
.239
.917
.817
.340
.815
.04.
89.
82.
919
.034
.642
.945
.05.
19.
427
.145
.332
.26.
314
.124
.718
.426
.04.
717
.227
.09.
123
.211
.217
.92.
935
.24.
549
.0
2.75
GE
P(1
,-2.
3,0)
25.5
23.1
12.4
12.4
23.7
11.5
4.2
7.5
2.6
13.8
21.4
25.1
25.3
4.4
6.8
16.8
30.8
18.4
5.5
10.4
15.5
11.2
18.1
6.2
10.5
17.3
8.1
14.4
9.4
12.5
2.7
25.8
3.8
26.9
2.75
GE
P(1
.5,-
1.4,
0)9.
48.
96.
97.
19.
26.
73.
04.
52.
27.
58.
38.
47.
93.
24.
18.
512
.97.
74.
05.
77.
45.
210
.47.
04.
98.
46.
16.
76.
67.
12.
212
.43.
28.
5
2.75
GE
P(2
,-0.
5,0)
5.8
5.6
4.7
5.0
5.8
4.6
2.4
3.3
2.1
5.2
5.1
5.2
4.9
2.6
3.0
6.1
7.4
5.4
3.2
3.8
4.9
3.4
7.6
6.1
3.2
5.7
5.1
4.3
5.2
5.3
1.9
7.3
3.2
4.9
2.75
GE
P(2
.3,0
,0)
4.9
4.8
4.1
4.3
5.0
3.9
2.1
2.9
2.1
4.5
4.5
4.8
4.7
2.2
2.6
5.5
5.9
5.0
2.9
3.2
4.3
3.0
6.8
5.7
2.8
4.9
4.6
3.7
4.6
4.7
1.9
6.0
3.4
4.3
2.75
GE
P(3
,0.8
,0)
4.5
4.2
3.1
3.3
4.3
2.8
1.6
2.2
1.9
3.7
4.7
5.5
5.6
1.7
2.0
5.0
4.3
4.7
2.4
2.2
3.5
2.4
5.9
4.8
2.2
3.9
3.6
3.1
3.9
4.0
1.8
4.3
4.1
4.3
2.75
GE
P(4
,1.6
,0)
4.9
4.4
2.4
2.6
4.5
1.9
1.2
1.6
1.8
3.5
6.2
7.7
7.9
1.2
1.7
4.6
3.8
4.5
2.0
1.6
3.2
2.2
5.3
4.1
2.1
3.4
3.0
2.7
3.4
3.8
2.0
3.8
5.1
5.4
2.75
GE
P(0
,690
,706
)43
.454
.946
.145
.755
.949
.055
.457
.366
.262
.142
.629
.922
.056
.060
.47.
363
.051
.242
.059
.452
.659
.526
.860
.160
.348
.927
.254
.461
.152
.254
.964
.069
.658
.5
3G
EP
(0.5
,-4.
6,0)
57.7
53.2
23.0
22.4
54.2
17.3
8.0
12.9
5.1
20.1
42.0
55.9
60.9
8.3
12.7
38.2
48.6
41.4
9.3
16.9
33.0
27.5
29.8
5.2
26.1
34.9
11.0
31.9
11.0
20.1
5.1
35.2
4.1
67.1
3G
EP
(0.6
,-3.
6,0)
49.2
44.3
20.3
19.9
45.4
15.7
7.9
11.8
5.2
17.3
35.4
47.5
52.2
8.3
11.7
32.6
42.7
34.1
9.0
15.2
27.9
23.3
25.6
5.5
22.2
29.7
10.6
26.9
10.1
17.1
5.2
31.7
3.7
58.9
3G
EP
(0.7
,-2.
9,0)
39.2
34.4
17.0
16.9
35.3
13.7
7.5
10.5
5.0
14.9
28.3
37.8
41.2
7.8
10.3
26.2
35.9
26.1
8.4
13.2
22.3
18.6
21.0
5.8
17.9
23.9
9.8
21.4
9.2
14.3
5.1
27.8
3.4
47.3
3G
EP
(0.8
,-2.
5,0)
29.2
25.1
14.4
14.3
25.9
12.2
7.3
9.7
5.0
12.4
21.6
28.0
30.0
7.6
9.2
20.3
28.3
18.8
8.1
11.7
17.6
14.9
17.0
6.1
14.3
18.9
9.2
17.0
8.4
11.9
5.1
22.9
3.3
34.6
3G
EP
(1,-
1.9,
0)15
.213
.210
.310
.413
.59.
36.
67.
94.
78.
611
.814
.214
.56.
87.
412
.016
.210
.07.
28.
711
.29.
711
.16.
49.
412
.08.
010
.86.
88.
34.
814
.52.
916
.5
3G
EP
(1.5
,-1,
0)6.
26.
06.
66.
56.
26.
35.
66.
04.
95.
65.
25.
45.
35.
85.
86.
36.
55.
45.
96.
16.
36.
06.
35.
76.
06.
66.
26.
15.
35.
64.
96.
53.
66.
4
3G
EP
(2,0
,0)
5.0
5.0
5.0
5.0
5.1
5.0
4.8
5.2
5.1
5.2
4.9
5.1
4.9
5.0
5.1
5.0
5.0
5.0
5.0
4.9
5.1
5.0
5.0
5.0
5.0
5.1
5.1
5.0
5.2
5.0
5.0
5.1
5.1
5.1
32
Tab
le4:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=50
(con
tinuin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3G
EP
(3,1
.4,0
)6.
25.
83.
73.
86.
03.
53.
84.
15.
45.
77.
88.
58.
24.
04.
44.
55.
75.
54.
13.
94.
64.
74.
24.
54.
74.
33.
74.
45.
05.
35.
65.
78.
26.
5
3G
EP
(0,6
65,6
61)
43.5
54.7
46.0
45.6
55.7
49.0
55.2
57.3
65.9
62.0
42.5
29.8
21.9
55.8
60.2
7.3
62.8
51.2
42.1
59.3
52.6
59.4
27.0
59.8
60.1
48.9
27.0
54.4
60.9
52.2
54.6
63.7
69.2
58.4
3.5
GE
P(0
.5,-
3.8,
0)38
.633
.120
.119
.934
.116
.313
.615
.110
.112
.923
.434
.840
.314
.014
.828
.227
.322
.813
.116
.524
.323
.318
.59.
422
.924
.912
.324
.310
.113
.210
.221
.23.
751
.8
3.5
GE
P(0
.6,-
2.8,
0)29
.825
.418
.117
.826
.215
.513
.814
.710
.411
.217
.826
.230
.414
.214
.522
.821
.316
.813
.015
.620
.620
.514
.89.
620
.320
.811
.920
.69.
811
.410
.817
.53.
741
.5
3.5
GE
P(0
.7,-
2.3,
0)21
.518
.416
.215
.719
.014
.513
.814
.310
.89.
912
.818
.120
.714
.214
.017
.115
.812
.012
.814
.717
.217
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.99.
717
.617
.211
.317
.39.
610
.011
.213
.94.
030
.2
3.5
GE
P(0
.8,-
1.9,
0)14
.213
.114
.713
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.514
.013
.914
.111
.39.
08.
811
.512
.914
.313
.911
.911
.38.
512
.514
.314
.415
.69.
59.
815
.714
.211
.014
.79.
79.
011
.810
.74.
721
.1
3.5
GE
P(1
,-1.
4,0)
7.9
8.8
12.4
11.5
9.0
12.7
13.7
13.5
12.4
8.6
5.6
6.1
6.2
14.1
13.5
7.2
7.7
6.6
11.9
13.4
11.6
13.4
6.6
9.8
13.6
11.0
9.9
12.0
9.9
8.3
12.8
7.9
6.8
12.9
3.5
GE
P(1
.6,0
,0)
7.7
9.2
10.2
9.1
9.5
11.3
13.2
13.2
15.2
11.3
8.3
7.4
6.5
13.7
13.8
4.7
10.5
8.2
10.8
13.4
10.3
12.7
4.9
10.7
13.0
9.2
8.1
10.8
12.3
9.3
15.6
10.4
14.3
11.6
3.5
GE
P(2
,0.8
,0)
9.4
10.9
9.6
8.7
11.3
11.0
13.2
13.3
16.6
13.3
11.3
10.2
9.0
13.6
14.1
4.5
13.1
9.5
10.5
13.7
10.5
13.2
4.7
11.6
13.5
9.3
7.7
11.1
13.6
10.3
17.1
12.9
17.9
13.2
3.5
GE
P(3
,2.3
,0)
14.3
15.8
8.9
8.5
16.3
10.2
12.7
13.4
19.2
18.2
19.6
17.5
15.1
13.2
15.1
5.1
19.3
12.9
10.1
14.1
12.2
15.1
5.1
13.9
15.4
10.5
6.3
12.6
16.1
13.2
20.2
19.2
25.7
17.7
3.5
GE
P(0
,620
,609
)43
.554
.645
.645
.355
.648
.754
.957
.065
.961
.842
.630
.022
.155
.659
.97.
462
.950
.941
.759
.252
.359
.226
.859
.759
.948
.527
.053
.960
.951
.954
.863
.869
.458
.3
4G
EP
(0.4
,-4.
5,0)
34.2
30.1
23.1
22.5
31.0
19.9
19.4
20.0
15.3
12.8
17.8
28.1
34.3
19.8
19.7
26.3
20.9
18.6
17.5
20.5
25.5
26.8
16.6
13.9
26.7
25.3
14.7
26.1
13.0
13.3
15.6
17.5
5.4
51.0
4G
EP
(0.5
,-3.
2,0)
27.2
24.1
21.4
20.6
24.9
19.3
19.6
19.9
16.0
12.1
13.8
21.3
26.0
20.0
19.7
21.7
16.7
14.6
17.4
20.1
22.8
24.6
14.0
14.2
24.6
22.3
14.3
23.4
13.3
12.5
16.3
14.8
5.8
42.6
4G
EP
(0.6
,-2.
3,0)
20.0
18.9
20.4
19.4
19.6
19.4
20.4
20.5
17.2
11.8
10.1
14.5
17.6
20.8
20.2
16.5
13.0
11.2
17.6
20.5
20.8
23.2
11.9
14.8
23.3
20.1
14.2
21.5
14.1
12.0
17.8
12.5
6.9
33.8
4G
EP
(0.7
,-1.
9,0)
13.9
15.1
19.3
18.1
15.6
19.4
21.0
20.9
18.5
11.9
7.4
9.4
10.9
21.4
20.7
11.6
10.9
9.3
17.7
20.8
18.8
21.7
9.8
15.4
21.9
17.9
13.8
19.7
15.1
12.1
19.2
11.1
8.9
25.5
4G
EP
(0.8
,-1.
5,0)
10.4
13.3
18.7
17.1
13.6
19.6
21.7
21.6
20.3
13.1
6.2
6.5
6.9
22.1
21.6
8.2
10.7
8.9
17.8
21.5
17.8
21.2
8.6
16.1
21.5
16.7
13.8
18.7
16.4
12.7
20.9
11.0
11.5
20.8
4G
EP
(1,-
1.1,
0)9.
212
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.615
.813
.219
.321
.922
.022
.415
.17.
05.
75.
322
.322
.25.
912
.910
.117
.522
.016
.920
.67.
717
.121
.115
.512
.817
.818
.413
.622
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.216
.318
.3
4G
EP
(1.4
,0,0
)13
.217
.417
.415
.817
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.323
.928
.021
.914
.010
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923
.924
.94.
821
.615
.117
.724
.518
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321
.223
.716
.512
.319
.623
.617
.128
.321
.627
.621
.5
4G
EP
(2,1
.5,0
)18
.422
.817
.916
.723
.620
.524
.425
.332
.228
.022
.017
.614
.425
.027
.25.
228
.819
.718
.226
.421
.226
.28.
124
.926
.818
.611
.822
.327
.620
.932
.629
.036
.226
.2
4G
EP
(3,3
.1,0
)25
.130
.018
.217
.930
.920
.825
.427
.237
.035
.532
.126
.020
.926
.130
.26.
037
.325
.618
.428
.924
.630
.29.
330
.030
.921
.311
.225
.832
.625
.537
.837
.845
.632
.5
4G
EP
(0,5
80,5
84)
43.4
54.8
45.8
45.6
55.9
48.9
55.3
57.2
66.1
62.1
42.5
29.9
22.1
55.9
60.2
7.2
62.8
51.0
41.9
59.3
52.6
59.5
26.8
60.0
60.2
48.8
27.0
54.2
60.8
52.1
54.7
63.8
69.3
58.2
4.5
GE
P(0
.4,-
4,0)
27.4
26.0
25.5
24.4
26.9
24.0
25.2
25.4
21.4
14.4
12.0
19.3
24.4
25.7
25.1
21.9
16.1
15.3
21.5
25.4
26.5
29.5
15.0
19.3
29.7
25.5
16.9
27.4
18.0
15.1
21.6
15.4
8.9
46.3
4.5
GE
P(0
.5,-
2.7,
0)21
.522
.225
.123
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.924
.526
.326
.323
.115
.19.
213
.717
.126
.826
.017
.414
.213
.122
.026
.325
.128
.613
.520
.229
.024
.016
.926
.119
.215
.523
.414
.510
.739
.4
4.5
GE
P(0
.6,-
2,0)
16.2
19.3
24.4
22.9
19.9
25.0
27.5
27.4
25.1
16.2
7.3
9.4
11.2
28.0
27.2
12.6
13.5
11.7
22.4
27.3
23.9
28.0
12.0
21.4
28.4
22.6
16.9
25.1
21.1
16.1
25.7
14.1
13.3
32.4
4.5
GE
P(0
.7,-
1.5,
0)12
.817
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.018
.225
.428
.428
.427
.418
.26.
86.
46.
828
.928
.48.
814
.912
.222
.528
.423
.127
.610
.722
.628
.021
.516
.524
.323
.217
.227
.915
.617
.527
.3
4.5
GE
P(0
.8,-
1.2,
0)12
.218
.323
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.718
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.129
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.830
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.48.
26.
15.
530
.130
.06.
418
.614
.423
.129
.923
.428
.210
.324
.628
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.616
.324
.626
.019
.130
.519
.022
.925
.5
4.5
GE
P(1
,-0.
8,0)
14.8
21.5
24.1
22.2
22.1
27.0
30.8
31.3
34.4
26.2
12.7
8.8
7.1
31.4
32.1
5.2
24.8
18.1
23.7
31.9
24.9
30.0
10.6
27.6
30.6
22.5
16.3
26.1
29.8
22.1
34.0
25.0
30.8
26.7
4.5
GE
P(1
.3,0
,0)
20.4
27.3
25.2
23.5
28.1
28.4
33.0
33.9
39.9
33.4
21.1
15.1
11.9
33.6
35.4
5.2
33.5
24.0
24.6
34.9
27.8
33.6
11.3
32.4
34.3
25.1
16.2
29.3
34.8
26.5
38.8
33.7
40.8
31.8
4.5
GE
P(2
,2.1
,0)
28.7
36.1
27.0
26.2
37.1
30.2
35.6
37.4
46.7
42.9
32.8
25.2
19.6
36.3
40.2
6.1
44.2
32.1
25.9
39.1
32.8
39.4
13.3
39.2
40.2
29.4
16.6
34.4
41.6
32.9
45.1
44.9
52.0
39.5
4.5
GE
P(3
,3.9
,0)
35.9
44.3
29.2
29.4
45.3
31.9
38.3
40.8
52.5
50.9
42.4
32.6
25.1
39.0
44.9
7.3
52.5
39.3
27.2
43.4
38.1
45.2
15.4
45.8
46.0
33.9
16.8
39.7
47.4
39.0
50.6
53.6
60.4
46.6
4.5
GE
P(0
,550
,557
)43
.855
.346
.245
.956
.249
.355
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.362
.442
.830
.122
.156
.160
.57.
263
.351
.342
.159
.652
.859
.826
.960
.260
.549
.127
.254
.561
.252
.455
.064
.269
.858
.7
5G
EP
(0.5
,-2.
4,0)
19.7
23.8
28.6
27.1
24.5
29.4
32.3
32.3
30.1
19.9
7.8
9.7
12.0
32.8
32.2
15.0
16.5
14.9
26.2
32.2
28.6
33.1
14.4
26.4
33.6
27.0
19.1
29.9
26.1
19.9
29.9
17.5
17.0
39.2
5G
EP
(0.6
,-1.
7,0)
16.5
22.8
29.1
27.1
23.3
30.7
34.3
34.2
33.2
22.7
7.4
6.9
7.6
34.8
34.4
10.3
18.8
15.4
27.1
34.3
28.6
33.9
13.7
28.6
34.4
26.6
19.4
30.1
29.0
21.7
33.2
19.7
21.9
34.6
5G
EP
(0.7
,-1.
3,0)
15.9
23.7
29.1
27.0
24.3
31.9
35.7
36.3
36.9
26.9
9.4
6.5
5.8
36.3
36.5
7.1
23.9
18.3
27.8
36.4
29.1
34.7
13.4
31.1
35.3
26.8
19.5
30.6
32.5
24.2
36.3
24.3
28.9
32.3
5G
EP
(0.8
,-1,
0)18
.026
.729
.727
.727
.333
.037
.438
.040
.932
.013
.68.
66.
638
.039
.05.
829
.922
.328
.538
.730
.736
.613
.734
.137
.328
.119
.632
.236
.027
.739
.430
.236
.032
.9
5G
EP
(1,-
0.6,
0)23
.132
.131
.429
.632
.934
.739
.841
.046
.338
.921
.214
.210
.740
.442
.55.
438
.428
.529
.941
.934
.040
.514
.839
.141
.331
.020
.035
.641
.232
.143
.738
.645
.437
.4
5G
EP
(1.1
,0,0
)28
.337
.532
.831
.538
.536
.341
.743
.350
.644
.728
.320
.015
.142
.445
.45.
845
.334
.031
.044
.837
.143
.816
.143
.244
.533
.820
.538
.845
.336
.047
.045
.752
.842
.0
5G
EP
(2,2
.7,0
)38
.047
.736
.436
.248
.739
.345
.747
.958
.154
.941
.030
.623
.346
.451
.37.
256
.143
.633
.550
.343
.850
.919
.551
.351
.839
.921
.445
.552
.943
.852
.757
.163
.650
.9
5G
EP
(3,4
.6,0
)43
.954
.539
.039
.655
.641
.648
.851
.563
.361
.549
.136
.627
.649
.555
.78.
162
.949
.835
.254
.348
.756
.122
.157
.056
.944
.422
.150
.558
.149
.557
.164
.170
.056
.7
5G
EP
(0,5
00,6
00)
43.7
54.8
46.0
45.6
55.8
49.0
55.3
57.4
66.1
62.1
42.6
30.0
22.0
55.9
60.4
7.2
63.0
51.0
42.0
59.4
52.5
59.4
27.0
60.0
60.2
48.9
27.1
54.3
61.0
52.3
54.7
64.0
69.5
58.2
6G
EP
(0.4
,-2.
9,0)
23.3
30.3
35.4
33.8
31.0
36.9
40.6
40.9
39.1
27.6
8.3
8.7
10.8
41.1
40.9
14.9
22.8
20.2
32.5
40.9
35.7
41.3
18.5
35.2
41.9
33.7
23.2
37.3
35.1
27.2
37.4
24.2
25.4
45.9
6G
EP
(0.5
,-1.
9,0)
22.4
31.6
37.0
35.2
32.3
39.3
43.5
44.1
43.7
32.5
9.4
6.9
7.4
44.1
44.3
11.4
28.0
23.1
34.3
44.2
37.4
43.4
18.9
39.0
44.0
35.1
24.0
39.1
39.6
30.6
41.4
28.9
32.5
43.8
6G
EP
(0.6
,-1.
3,0)
23.4
34.1
38.3
36.3
34.8
41.4
46.1
47.0
48.6
38.7
13.2
7.5
6.1
46.7
47.7
8.0
35.4
28.0
36.0
47.6
39.2
45.6
19.5
43.0
46.3
36.5
24.6
41.0
44.4
34.9
45.1
36.0
41.3
42.9
6G
EP
(0.8
,-0.
8,0)
31.5
42.9
41.2
39.8
43.8
44.9
50.4
51.7
57.2
50.1
25.9
15.7
11.0
51.0
53.6
6.1
49.5
38.8
38.5
53.0
44.7
51.5
22.1
50.8
52.2
41.4
25.5
46.4
52.4
42.9
50.4
49.8
56.2
48.1
6G
EP
(1,0
,0)
43.3
54.5
45.6
45.3
55.5
48.7
54.8
56.9
65.6
61.8
42.5
30.0
22.2
55.4
59.9
7.4
62.8
50.8
41.6
59.0
52.2
59.1
26.5
59.7
59.9
48.4
26.8
54.0
60.8
51.8
54.9
63.8
69.4
57.9
6G
EP
(2,3
.9,0
)52
.063
.350
.651
.164
.353
.159
.962
.572
.570
.152
.337
.927
.960
.566
.18.
670
.959
.445
.465
.059
.466
.231
.567
.066
.955
.429
.161
.067
.559
.658
.072
.276
.965
.8
6G
EP
(3,6
.2,0
)55
.267
.053
.154
.268
.055
.362
.565
.275
.373
.556
.240
.629
.663
.169
.19.
474
.363
.147
.067
.862
.669
.233
.870
.469
.958
.530
.364
.270
.763
.059
.775
.679
.769
.0
6G
EP
(0,1
40,1
29.1
)44
.455
.646
.646
.356
.749
.755
.957
.866
.762
.843
.330
.222
.356
.560
.87.
363
.652
.042
.460
.053
.360
.127
.660
.660
.849
.627
.655
.061
.752
.955
.164
.670
.259
.0
10G
EP
(0.4
,-1.
7,0)
46.4
59.9
58.7
58.1
60.7
61.6
66.8
68.4
71.6
65.1
27.7
12.7
8.1
67.4
69.8
10.4
62.6
53.8
53.8
69.3
62.1
68.3
38.0
67.6
68.9
59.1
36.1
63.7
68.3
60.0
53.6
63.1
68.0
65.8
10G
EP
(0.5
,-1,
0)56
.168
.663
.363
.369
.465
.971
.473
.278
.574
.743
.223
.514
.371
.975
.39.
173
.764
.557
.774
.668
.574
.143
.774
.674
.765
.438
.470
.075
.068
.153
.874
.478
.671
.7
10G
EP
(0.7
,0,0
)77
.786
.073
.875
.586
.574
.079
.781
.789
.489
.275
.759
.345
.680
.185
.014
.289
.383
.265
.583
.982
.086
.158
.586
.986
.579
.342
.983
.186
.182
.347
.690
.892
.186
.3
10G
EP
(1.4
,5.7
,0)
67.4
77.9
68.2
69.0
78.7
69.7
75.4
77.4
84.5
82.8
62.3
43.8
31.6
75.8
80.2
10.4
83.1
75.0
61.3
79.2
75.3
80.2
50.6
81.1
80.7
72.2
40.6
76.6
80.8
75.3
51.4
84.3
87.0
79.4
10G
EP
(0,6
,12.
2)62
.073
.363
.664
.274
.165
.571
.373
.280
.978
.757
.239
.928
.671
.876
.39.
579
.370
.157
.475
.370
.676
.045
.276
.876
.667
.437
.572
.176
.970
.653
.180
.383
.775
.2
10G
EP
(0,1
7,-1
2.6)
62.8
73.7
64.3
64.9
74.5
66.1
71.9
74.0
81.3
79.2
57.6
40.3
28.9
72.4
76.8
9.6
79.7
70.6
57.9
75.9
71.2
76.6
45.8
77.4
77.2
68.0
38.0
72.6
77.4
71.2
52.8
80.8
84.0
75.9
20G
EP
(0.3
,-1.
3,0)
79.7
87.8
81.3
82.2
88.3
82.1
86.2
87.6
91.8
91.0
68.3
42.0
25.3
86.5
89.6
13.9
90.5
85.4
74.5
88.9
86.3
89.5
67.6
90.1
89.9
84.3
50.3
87.2
89.7
86.7
40.8
91.2
92.8
88.4
20G
EP
(0.5
,0,0
)95
.397
.891
.493
.197
.989
.693
.194
.398
.098
.294
.485
.473
.193
.396
.228
.198
.096
.783
.395
.696
.197
.285
.397
.597
.395
.157
.796
.496
.696
.023
.098
.898
.697
.4
20G
EP
(0.8
,2.3
,0)
88.7
93.8
86.6
88.0
94.1
86.1
89.9
91.2
95.6
95.5
84.4
66.5
49.9
90.2
93.3
18.0
95.4
92.3
79.1
92.6
91.8
94.0
76.7
94.5
94.2
90.3
54.1
92.4
93.8
92.1
32.4
96.2
96.8
93.8
20G
EP
(0,1
4,-1
7.6)
77.7
86.0
77.6
78.7
86.5
78.3
83.1
84.7
90.3
89.4
71.0
50.8
36.3
83.4
87.1
12.5
89.4
83.8
70.6
86.3
83.6
87.3
63.1
88.0
87.7
81.4
47.3
84.6
87.5
83.9
43.0
90.5
92.0
86.8
20G
EP
(0,6
,2.6
)73
.682
.873
.974
.983
.474
.979
.981
.888
.086
.866
.847
.233
.780
.384
.311
.687
.080
.267
.183
.580
.384
.458
.285
.284
.977
.744
.581
.484
.980
.446
.288
.190
.183
.9
50G
EP
(0.3
,-0.
7,0)
97.3
98.8
95.2
96.2
98.8
94.0
96.2
96.9
98.9
99.1
95.8
85.5
70.1
96.3
98.0
30.4
98.9
98.2
89.4
97.7
97.9
98.5
91.5
98.7
98.6
97.4
64.2
98.1
98.2
97.9
14.6
99.3
99.3
98.5
50G
EP
(0.4
,0,0
)99
.499
.898
.098
.699
.896
.698
.198
.599
.799
.899
.296
.691
.198
.199
.347
.399
.699
.693
.299
.099
.499
.696
.799
.799
.799
.268
.899
.599
.499
.46.
999
.999
.899
.6
50G
EP
(0.6
,1.2
,0)
98.7
99.5
97.3
98.0
99.5
96.1
97.8
98.2
99.5
99.6
97.9
90.9
78.5
97.8
99.0
37.1
99.5
99.2
92.6
98.8
99.0
99.3
95.0
99.4
99.4
98.7
68.1
99.1
99.1
99.0
9.4
99.7
99.7
99.3
50G
EP
(0,5
.1,2
.1)
78.6
86.7
78.5
79.6
87.3
79.1
83.8
85.3
90.7
90.0
71.5
51.6
36.8
84.1
87.7
12.7
90.1
84.5
71.6
86.9
84.5
87.9
64.3
88.7
88.3
82.3
48.0
85.4
88.1
84.7
41.8
91.0
92.5
87.4
50G
EP
(0,8
,-7.
2)85
.691
.784
.685
.892
.084
.788
.689
.994
.393
.879
.058
.442
.288
.991
.915
.093
.889
.977
.991
.289
.792
.373
.492
.992
.588
.052
.690
.492
.290
.034
.794
.795
.591
.9
50G
EP
(0,1
0,-1
3.8)
90.2
94.7
88.9
90.0
95.0
88.5
91.7
92.8
96.3
96.2
85.1
66.4
48.9
91.9
94.5
18.3
96.0
93.4
82.1
93.9
93.1
94.9
80.2
95.3
95.1
91.8
56.8
93.6
94.8
93.3
28.2
96.7
97.1
94.6
50G
EP
(0,1
0.8,
-17.
3)93
.997
.092
.193
.397
.291
.394
.195
.097
.897
.990
.473
.956
.194
.296
.522
.297
.796
.185
.996
.095
.897
.085
.797
.397
.194
.860
.696
.196
.695
.922
.598
.398
.496
.8
Mea
n
5046
.751
.744
.743
.252
.342
.031
.542
.626
.448
.944
.140
.236
.632
.143
.625
.054
.747
.423
.147
.048
.646
.843
.333
.946
.348
.726
.948
.247
.345
.518
.750
.643
.154
.8
Ran
k
5014
417
213
2429
2331
618
2526
2819
322
1033
128
1320
2715
730
911
1634
522
1
Dev
.to
the
Bes
t-
Mea
n
5014
.69.
616
.718
.19.
119
.329
.918
.834
.912
.417
.221
.124
.729
.217
.736
.36.
713
.938
.314
.412
.714
.518
.127
.515
.112
.634
.513
.114
.115
.842
.610
.718
.26.
5
Ran
k
5014
417
20.5
324
2923
316
1825
2628
1932
210
3312
813
20.5
2715
730
911
1634
522
1
Dev
.to
the
Bes
t-
Max
5063
.340
.147
.249
.639
.463
.095
.865
.899
.947
.662
.775
.079
.695
.064
.780
.531
.151
.792
.855
.134
.151
.247
.999
.556
.132
.283
.036
.063
.147
.499
.933
.579
.638
.1
Ran
k
5021
89
137
1931
2333
.511
1824
25.5
3022
271
1529
164
1412
3217
228
520
1033
.53
25.5
6
33
Tab
le5:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=10
0(b
egin
nin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
1.1
GE
P(1
,-40
.5,0
)10
010
010
010
010
00.
810
010
010
010
010
010
010
010
010
093
.010
010
038
.910
010
010
010
010
010
010
099
.210
010
010
03.
897
.410
010
0
1.1
GE
P(4
,-18
.1,0
)10
010
010
010
010
00.
910
010
010
010
010
010
010
010
010
094
.610
010
063
.510
010
010
010
010
010
010
099
.910
010
010
03.
297
.810
010
0
1.1
GE
P(6
,-14
.6,0
)10
010
010
010
010
00.
810
010
010
010
010
010
010
010
010
096
.010
010
075
.510
010
010
010
010
010
010
010
010
010
010
02.
998
.110
010
0
1.1
GE
P(8
,-12
.9,0
)10
010
010
010
010
00.
910
010
010
010
010
010
010
010
010
097
.010
010
083
.110
010
010
010
010
010
010
010
010
010
010
02.
898
.210
010
0
1.1
GE
P(1
5,-1
0.9,
0)10
010
010
010
010
00.
910
010
010
010
010
010
010
010
010
098
.910
010
090
.810
010
010
010
099
.910
010
010
010
010
010
03.
098
.410
010
0
1.1
GE
P(3
0,-1
0,0)
100
100
100
100
100
0.9
100
100
100
100
100
100
100
100
100
99.6
100
100
93.7
100
100
100
100
99.9
100
100
100
100
100
100
3.0
98.6
100
100
1.1
GE
P(6
0,-9
.8,0
)10
010
010
010
010
00.
910
010
010
010
010
010
010
010
010
099
.810
010
094
.410
010
010
010
099
.910
010
010
010
010
010
02.
898
.710
010
0
1.5
GE
P(1
,-8.
3,0)
100
100
100
100
100
91.9
99.7
99.9
86.8
100
100
100
100
99.7
100
92.3
100
100
60.6
100
100
100
100
0.3
100
100
55.1
100
100
100
0.0
98.5
79.3
100
1.5
GE
P(2
,-5.
7,0)
100
100
100
100
100
95.6
100
100
88.1
100
100
100
100
100
100
88.0
100
100
72.8
100
100
100
100
0.2
100
100
67.3
100
100
100
0.0
99.1
90.9
100
1.5
GE
P(4
,-3.
7,0)
100
100
100
100
100
97.2
100
100
87.4
100
100
100
100
100
100
81.8
100
100
75.7
100
100
100
100
8.6
100
100
85.4
100
100
100
0.0
99.6
99.1
100
1.5
GE
P(6
,-2.
9,0)
100
100
100
100
100
97.4
100
100
84.4
100
100
100
99.7
100
100
83.1
100
100
74.9
100
100
100
100
21.2
100
100
93.5
100
100
100
0.0
99.7
99.9
100
1.5
GE
P(8
,-2.
5,0)
100
100
100
100
100
97.4
100
100
82.0
100
100
99.8
98.8
100
100
84.9
100
100
74.1
100
100
100
100
28.5
100
100
96.9
100
100
100
0.0
99.8
100
100
1.5
GE
P(1
5,-2
.1,0
)99
.810
010
010
010
097
.510
010
078
.110
010
099
.195
.610
010
086
.310
010
072
.810
010
010
010
037
.710
010
099
.210
010
010
00.
099
.810
010
0
1.5
GE
P(3
0,-1
.9,0
)99
.810
010
010
010
097
.510
010
076
.010
099
.998
.693
.010
010
086
.310
010
072
.710
010
010
010
040
.710
010
099
.710
010
010
00.
099
.810
010
0
1.5
GE
P(6
0,-1
.8,0
)99
.710
010
010
010
097
.510
010
075
.310
099
.998
.291
.910
010
086
.210
010
072
.510
010
010
010
041
.510
010
099
.810
010
010
00.
099
.810
010
0
1.84
GE
P(0
.6,-
8.4,
0)10
010
099
.799
.510
094
.674
.689
.324
.199
.910
010
010
073
.396
.091
.110
010
028
.897
.210
010
010
00.
210
010
026
.010
090
.499
.90.
097
.026
.910
0
1.84
GE
P(0
.8,-
6,0)
100
100
99.5
99.2
100
95.1
74.0
89.7
20.9
99.8
100
100
100
72.6
95.6
89.7
100
100
28.3
97.2
100
100
100
0.2
100
100
26.6
100
91.2
99.9
0.0
97.1
27.5
99.9
1.84
GE
P(1
,-5,
0)10
010
099
.198
.610
095
.873
.289
.917
.599
.810
010
010
071
.795
.386
.010
010
028
.197
.310
010
099
.91.
110
010
027
.510
092
.599
.90.
097
.428
.599
.9
1.84
GE
P(1
.5,-
3.9,
0)99
.810
097
.796
.410
097
.171
.490
.710
.299
.810
099
.999
.969
.694
.569
.999
.910
025
.797
.499
.799
.299
.716
.299
.099
.830
.799
.795
.299
.60.
098
.133
.099
.8
1.84
GE
P(2
,-3.
2,0)
98.6
99.8
96.6
95.0
99.8
98.0
70.6
91.4
6.2
99.6
99.7
99.3
98.4
68.5
94.0
57.3
99.9
99.7
23.0
97.6
99.1
97.1
99.4
42.2
96.5
99.4
34.8
98.8
96.9
99.3
0.0
98.3
38.3
99.5
1.84
GE
P(3
,-2.
1,0)
91.0
98.5
95.8
94.2
98.5
98.8
68.8
92.0
2.9
99.2
97.0
92.0
84.7
66.4
92.9
45.4
99.6
97.8
19.1
97.4
97.5
92.4
99.0
74.8
90.9
98.4
42.0
96.8
98.5
98.2
0.0
98.3
49.4
97.9
1.84
GE
P(4
,-1.
4,0)
81.9
96.5
96.1
94.8
96.5
99.0
67.3
92.0
1.7
98.6
91.2
78.8
64.8
64.8
91.7
40.6
98.9
94.1
16.6
97.3
96.5
89.3
99.0
86.3
87.3
97.8
48.9
95.5
99.0
96.9
0.0
97.8
59.7
95.7
1.84
GE
P(6
,-0.
7,0)
69.9
93.8
97.4
96.8
93.8
99.1
66.7
92.0
0.9
97.7
79.4
56.6
39.0
64.1
90.4
36.7
97.0
87.8
14.7
97.0
96.6
87.8
99.4
92.6
85.3
98.0
61.4
95.3
99.5
95.0
0.0
96.0
76.0
92.7
1.84
GE
P(8
,-0.
4,0)
62.7
92.2
98.3
98.1
92.3
99.2
65.5
91.9
0.7
96.9
70.1
43.3
27.1
62.7
89.5
34.4
95.3
83.0
13.4
96.7
97.0
87.9
99.6
94.3
85.3
98.3
70.1
95.8
99.7
93.6
0.0
94.5
85.5
90.9
1.84
GE
P(1
5.2,
0,0)
54.1
90.7
99.2
99.2
90.7
99.1
64.5
91.4
0.4
95.7
56.7
28.5
15.9
61.7
88.0
29.7
92.0
75.5
12.2
96.3
98.1
90.1
99.9
95.3
87.4
99.0
84.4
97.0
99.8
91.2
0.0
91.5
95.9
88.5
2G
EP
(0.5
,-8.
9,0)
100
100
97.8
97.0
100
85.0
52.9
75.0
10.2
98.7
100
100
100
51.1
85.7
90.2
99.9
100
20.3
90.7
100
100
99.7
0.4
100
100
20.0
100
76.9
99.1
0.1
95.5
15.1
99.9
2G
EP
(0.8
,-5.
1,0)
100
100
95.2
93.6
100
85.4
48.8
73.5
6.4
98.3
100
100
100
47.0
82.8
85.7
99.9
100
18.5
89.5
99.8
99.6
99.2
1.3
99.5
99.8
19.9
99.8
78.0
98.5
0.1
95.8
15.0
99.8
2G
EP
(1,-
4.2,
0)99
.910
092
.289
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086
.045
.271
.94.
297
.999
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010
043
.280
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198
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.279
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096
.115
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2G
EP
(1.5
,-3.
2,0)
96.6
99.0
84.1
80.6
99.0
86.7
38.4
69.3
1.5
96.3
98.7
98.5
97.6
36.3
74.5
54.4
99.5
98.7
12.8
86.7
94.6
89.0
95.0
31.2
87.4
95.8
22.2
93.8
82.8
94.4
0.0
96.3
17.0
98.4
2G
EP
(2,-
2.5,
0)86
.795
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694
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095
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2G
EP
(3,-
1.4,
0)64
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289
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.128
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482
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092
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2G
EP
(4,-
0.7,
0)50
.075
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184
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080
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086
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2G
EP
(6,0
,0)
35.0
65.4
80.3
78.9
65.4
88.8
23.0
60.1
0.0
78.6
40.0
21.6
13.1
20.9
54.9
19.5
78.3
54.0
4.6
78.6
75.6
51.3
92.1
88.0
46.7
82.1
41.8
70.7
92.8
68.6
0.0
77.7
44.6
65.3
2G
EP
(8,0
.3,0
)29
.562
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075
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520
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277
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072
.255
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2G
EP
(15,
0.7,
0)22
.858
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.290
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070
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45.
418
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.763
.637
.83.
475
.382
.355
.397
.387
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.888
.564
.076
.895
.759
.10.
064
.174
.358
.4
2G
EP
(0,8
65,8
73)
70.7
82.7
69.6
68.9
82.8
72.5
80.2
81.0
89.1
87.6
70.6
53.3
40.3
80.0
83.6
13.0
90.4
82.8
57.1
84.8
80.0
84.0
49.2
87.3
84.7
76.2
36.5
81.0
86.2
80.4
74.5
91.0
94.1
85.7
2.25
GE
P(0
.5,-
7.2,
0)10
010
084
.882
.810
064
.425
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590
.499
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010
024
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.186
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.399
.812
.871
.299
.098
.495
.81.
498
.199
.114
.999
.052
.891
.20.
591
.76.
299
.6
2.25
GE
P(0
.7,-
4.7,
0)99
.999
.977
.975
.199
.962
.321
.645
.71.
587
.999
.599
.999
.920
.354
.381
.298
.999
.510
.967
.597
.095
.092
.52.
894
.497
.314
.196
.951
.987
.70.
491
.35.
999
.3
2.25
GE
P(0
.8,-
3.8,
0)99
.399
.670
.367
.599
.660
.018
.142
.10.
985
.398
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.699
.717
.048
.972
.898
.698
.79.
263
.693
.188
.888
.26.
187
.794
.013
.792
.751
.083
.60.
391
.05.
498
.9
2.25
GE
P(1
,-3.
3,0)
96.5
98.0
62.6
59.6
98.0
58.5
15.3
39.2
0.6
81.9
96.7
98.2
98.3
14.1
44.0
61.1
97.7
96.4
8.0
60.3
86.1
78.7
82.6
11.9
76.8
88.0
13.2
85.2
51.0
78.6
0.2
90.3
5.4
97.6
2.25
GE
P(1
.5,-
2.4,
0)70
.479
.144
.242
.679
.253
.08.
730
.40.
269
.579
.878
.874
.77.
931
.032
.090
.276
.84.
649
.859
.945
.265
.732
.642
.364
.713
.157
.450
.461
.30.
184
.65.
479
.9
2.25
GE
P(2
,-1.
7,0)
46.5
58.4
36.1
35.5
58.5
49.6
5.7
25.2
0.1
59.0
57.6
51.3
44.0
5.1
23.8
20.8
78.3
56.2
3.3
43.4
44.7
28.6
57.3
43.4
25.9
50.8
13.4
41.4
50.1
48.9
0.0
74.7
5.6
57.0
2.25
GE
P(3
,-0.
5,0)
23.3
35.7
31.2
31.1
35.7
45.9
3.5
19.8
0.0
44.4
29.0
20.2
14.6
3.0
16.8
13.2
56.1
32.4
2.1
35.7
32.5
16.7
51.4
51.5
14.4
39.2
14.6
28.7
50.6
34.7
0.0
55.2
6.9
34.1
2.25
GE
P(3
.7,0
,0)
16.9
28.5
30.3
30.5
28.5
43.9
2.8
17.4
0.0
37.9
19.4
12.3
8.6
2.4
14.2
11.2
45.5
24.7
1.7
32.4
29.1
13.5
50.9
52.7
11.6
36.1
15.6
25.1
50.7
29.0
0.0
45.3
7.6
28.1
2.25
GE
P(4
,0.2
,0)
14.6
26.0
30.5
30.9
25.9
43.4
2.5
16.8
0.0
35.4
16.3
9.8
6.9
2.2
13.3
10.5
41.4
21.8
1.7
31.2
28.3
12.6
51.5
52.7
10.7
35.4
16.2
24.2
51.0
27.0
0.0
41.5
8.2
26.0
2.25
GE
P(8
,1.2
,0)
7.3
16.8
37.3
37.7
16.6
40.2
1.4
12.6
0.0
22.7
5.3
4.6
5.0
1.2
8.8
6.6
22.0
11.0
0.9
25.1
28.7
10.3
61.1
50.0
8.3
37.4
22.4
23.3
54.6
17.1
0.0
22.7
15.3
21.1
2.25
GE
P(0
,785
,782
)70
.782
.769
.668
.982
.872
.580
.181
.089
.087
.570
.853
.340
.279
.983
.313
.190
.282
.657
.284
.779
.883
.949
.287
.184
.676
.036
.980
.986
.180
.374
.790
.894
.085
.6
2.5
GE
P(0
.5,-
6.1,
0)99
.799
.864
.362
.599
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.113
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.61.
972
.798
.299
.799
.812
.737
.581
.896
.197
.910
.049
.292
.989
.982
.93.
189
.193
.312
.892
.832
.972
.61.
584
.62.
798
.8
2.5
GE
P(0
.7,-
3.9,
0)97
.898
.352
.250
.698
.339
.49.
925
.61.
465
.795
.198
.498
.99.
330
.171
.494
.094
.78.
142
.282
.776
.672
.74.
775
.184
.011
.482
.230
.363
.31.
282
.22.
297
.7
2.5
GE
P(0
.8,-
3.2,
0)91
.392
.741
.840
.992
.735
.47.
621
.81.
158
.989
.194
.795
.77.
124
.357
.990
.687
.76.
936
.469
.360
.562
.38.
058
.671
.710
.768
.328
.454
.50.
979
.42.
195
.0
2.5
GE
P(1
,-2.
7,0)
78.0
80.5
32.7
32.4
80.6
31.6
5.6
18.0
0.9
51.7
79.1
85.6
86.3
5.2
18.9
43.2
84.2
75.0
5.7
30.8
53.8
43.4
51.7
12.3
41.3
57.2
10.0
52.3
26.8
45.5
0.7
74.5
1.8
86.5
2.5
GE
P(1
.5,-
1.8,
0)35
.539
.117
.618
.839
.123
.22.
511
.10.
532
.941
.841
.738
.52.
39.
618
.056
.836
.23.
419
.024
.815
.431
.820
.514
.128
.78.
522
.822
.925
.90.
352
.91.
540
.4
2.5
GE
P(2
,-1,
0)17
.921
.212
.514
.021
.218
.21.
37.
60.
422
.321
.218
.415
.41.
25.
611
.036
.519
.52.
313
.315
.07.
724
.722
.16.
718
.67.
913
.120
.217
.00.
235
.51.
519
.2
2.5
GE
P(2
.8,0
,0)
8.4
11.2
9.4
10.9
11.1
14.1
0.7
5.0
0.2
13.7
9.0
7.1
5.9
0.6
3.2
7.3
19.6
10.4
1.5
9.0
9.7
3.9
20.7
21.0
3.3
12.7
7.2
8.0
17.9
10.7
0.1
19.8
1.6
9.8
2.5
GE
P(3
,0.2
,0)
7.4
9.9
9.1
10.5
9.8
13.5
0.6
4.6
0.2
12.3
7.5
6.0
5.1
0.5
2.8
6.8
17.1
9.2
1.4
8.2
8.9
3.4
20.3
20.7
2.9
12.1
7.3
7.3
17.6
9.8
0.1
17.3
1.7
8.9
2.5
GE
P(4
,0.9
,0)
5.2
6.9
8.5
9.6
6.8
11.2
0.3
3.4
0.1
8.2
4.6
4.8
5.0
0.3
1.8
5.5
9.9
6.4
1.0
6.2
7.5
2.4
20.2
18.4
2.0
10.6
7.2
5.9
16.3
7.1
0.1
10.2
2.1
7.9
2.5
GE
P(8
,1.9
,0)
5.0
6.2
10.1
10.6
6.0
8.0
0.1
1.9
0.1
3.7
6.3
10.7
12.2
0.1
0.9
4.3
4.0
4.5
0.7
3.5
8.0
2.1
26.8
13.5
1.7
11.5
8.4
5.7
15.1
4.4
0.1
4.3
4.1
12.0
2.5
GE
P(0
,730
,739
)70
.882
.769
.468
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.380
.080
.989
.087
.670
.853
.740
.579
.883
.412
.890
.382
.757
.284
.779
.883
.949
.287
.184
.675
.936
.780
.886
.280
.474
.590
.994
.085
.5
2.75
GE
P(0
.5,-
5.3,
0)97
.797
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.245
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.930
.310
.620
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352
.192
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.099
.010
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.291
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.233
.279
.274
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073
.279
.912
.279
.120
.250
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473
.51.
297
.5
2.75
GE
P(0
.6,-
4.1,
0)95
.095
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.139
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218
.52.
947
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.097
.68.
821
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329
.371
.065
.157
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363
.772
.011
.370
.718
.645
.03.
071
.01.
196
.3
2.75
GE
P(0
.7,-
3.3,
0)88
.788
.633
.433
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.624
.68.
116
.22.
842
.081
.591
.894
.37.
918
.260
.280
.779
.98.
525
.560
.253
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152
.061
.810
.959
.716
.938
.82.
967
.11.
093
.6
2.75
GE
P(0
.8,-
2.8,
0)78
.177
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.527
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114
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636
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915
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.274
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821
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339
.850
.310
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.415
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662
.10.
888
.2
2.75
GE
P(1
,-2.
3,0)
49.4
48.1
18.2
18.8
48.1
16.9
5.5
10.3
2.3
26.1
49.1
58.4
60.3
5.4
10.4
28.3
55.3
41.4
6.4
15.5
28.1
22.2
26.4
9.4
21.3
30.4
8.9
27.2
13.1
21.6
2.3
48.7
0.7
61.2
2.75
GE
P(1
.5,-
1.4,
0)15
.114
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69.
614
.79.
73.
25.
81.
712
.416
.116
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14.
910
.622
.912
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37.
510
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013
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611
.96.
69.
59.
110
.21.
522
.00.
815
.4
2.75
GE
P(2
,-0.
5,0)
7.1
7.2
5.5
6.7
7.1
6.4
2.1
3.7
1.5
7.3
7.1
6.8
6.1
2.1
2.8
6.6
11.1
7.0
3.1
4.4
5.9
3.6
10.0
8.7
3.4
7.2
5.4
5.2
7.1
6.4
1.2
11.1
1.1
6.1
2.75
GE
P(2
.3,0
,0)
5.5
5.7
4.5
5.6
5.5
5.3
1.7
3.0
1.4
5.7
5.3
5.2
4.9
1.7
2.2
5.5
7.7
5.7
2.7
3.4
4.8
2.7
8.9
7.8
2.6
5.9
4.8
4.1
6.4
5.5
1.1
7.9
1.6
4.6
2.75
GE
P(3
,0.8
,0)
4.6
4.5
3.4
4.4
4.3
3.6
1.1
2.2
1.2
4.1
4.8
5.7
5.9
1.0
1.4
4.8
4.5
4.7
2.1
2.0
3.7
1.9
8.2
6.1
1.8
4.7
4.1
3.1
5.2
4.4
1.0
4.6
2.9
4.4
2.75
GE
P(4
,1.6
,0)
5.6
5.1
2.9
3.7
5.0
2.4
0.7
1.5
1.2
3.4
7.4
9.7
10.3
0.7
1.0
4.4
3.9
4.7
1.6
1.2
3.6
1.8
8.2
4.7
1.7
4.4
3.5
2.9
4.1
4.0
1.0
3.9
5.2
7.0
2.75
GE
P(0
,690
,706
)70
.882
.769
.769
.082
.872
.580
.281
.089
.187
.670
.853
.540
.380
.083
.412
.990
.482
.857
.384
.880
.084
.149
.287
.284
.876
.136
.781
.086
.380
.374
.791
.094
.185
.8
3G
EP
(0.5
,-4.
6,0)
91.9
91.4
35.7
35.9
91.5
23.0
12.1
17.6
5.5
35.1
80.6
93.3
96.2
11.8
20.1
68.3
74.7
79.9
11.6
24.6
63.4
59.4
45.7
7.1
58.4
64.0
12.8
63.6
13.5
33.3
6.0
59.6
0.7
95.4
3G
EP
(0.6
,-3.
6,0)
85.1
83.6
30.1
30.3
83.7
20.5
11.3
15.7
5.4
30.0
72.4
87.6
91.9
11.1
17.6
60.6
68.6
71.0
11.1
21.4
53.3
48.9
38.3
7.2
48.0
54.0
11.9
53.4
12.2
27.7
6.0
55.1
0.6
92.7
3G
EP
(0.7
,-2.
9,0)
72.5
69.9
24.8
25.0
69.9
17.9
10.4
14.0
5.3
24.8
61.2
77.7
83.2
10.3
15.3
49.1
59.7
57.6
10.4
18.2
41.6
38.0
30.1
7.3
37.2
42.5
11.1
41.6
10.7
22.4
5.8
48.5
0.6
86.5
3G
EP
(0.8
,-2.
5,0)
56.2
52.2
20.1
20.2
52.2
15.7
9.7
12.5
5.1
20.2
48.0
63.2
68.4
9.6
13.2
36.7
48.9
42.1
9.7
15.6
30.7
27.8
23.0
7.7
27.2
31.7
10.5
30.7
9.9
17.7
5.8
41.0
0.6
73.6
3G
EP
(1,-
1.9,
0)27
.023
.813
.313
.323
.711
.58.
39.
85.
012
.424
.532
.034
.38.
29.
818
.227
.418
.58.
211
.116
.415
.113
.17.
614
.917
.18.
916
.47.
710
.75.
424
.80.
737
.0
3G
EP
(1.5
,-1,
0)7.
26.
97.
27.
06.
77.
26.
36.
65.
06.
26.
67.
16.
96.
26.
46.
97.
96.
15.
96.
87.
06.
86.
56.
26.
87.
26.
56.
95.
86.
05.
08.
02.
48.
2
3G
EP
(2,0
,0)
5.2
5.1
4.9
4.9
4.9
5.0
5.1
5.1
5.0
5.1
5.1
5.3
5.0
5.0
4.8
5.0
5.0
5.2
4.9
5.0
4.9
4.9
5.0
5.0
5.0
5.0
4.8
4.9
5.0
5.2
5.0
5.2
5.1
5.0
34
Tab
le5:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=10
0(c
onti
nuin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3G
EP
(3,1
.4,0
)7.
56.
83.
03.
46.
73.
13.
53.
45.
56.
210
.011
.411
.03.
53.
54.
57.
06.
03.
73.
44.
54.
24.
54.
54.
34.
33.
24.
24.
55.
45.
47.
211
.78.
0
3G
EP
(0,6
65,6
61)
70.8
82.8
69.5
68.8
82.9
72.4
80.2
80.9
89.0
87.6
71.0
53.7
40.7
80.0
83.5
12.7
90.3
82.7
57.5
84.7
79.8
84.0
49.3
87.2
84.7
76.0
36.5
80.9
86.1
80.4
74.7
90.9
94.1
85.6
3.5
GE
P(0
.5,-
3.8,
0)70
.667
.229
.128
.567
.421
.620
.321
.112
.716
.649
.672
.481
.420
.122
.254
.442
.449
.517
.023
.442
.843
.324
.413
.643
.241
.915
.443
.812
.816
.414
.833
.21.
488
.7
3.5
GE
P(0
.6,-
2.8,
0)56
.251
.525
.624
.451
.620
.120
.020
.412
.913
.437
.158
.468
.319
.821
.144
.033
.036
.516
.222
.034
.235
.518
.513
.335
.633
.214
.635
.212
.613
.515
.226
.51.
780
.9
3.5
GE
P(0
.7,-
2.3,
0)39
.034
.222
.620
.934
.219
.119
.919
.813
.611
.125
.040
.648
.919
.820
.431
.422
.722
.815
.821
.126
.828
.713
.613
.329
.125
.613
.927
.812
.711
.316
.219
.32.
365
.1
3.5
GE
P(0
.8,-
1.9,
0)23
.520
.819
.917
.720
.718
.319
.919
.614
.69.
515
.424
.329
.119
.719
.820
.014
.513
.415
.220
.421
.123
.79.
813
.224
.119
.813
.122
.113
.010
.017
.113
.53.
544
.4
3.5
GE
P(1
,-1.
4,0)
9.6
10.7
16.4
13.7
10.4
16.9
19.5
18.7
16.5
9.1
6.5
8.2
9.1
19.4
18.8
8.9
8.3
7.5
14.0
19.7
15.6
18.6
6.3
13.4
19.2
14.1
11.8
16.5
14.1
9.2
19.0
8.6
7.8
21.6
3.5
GE
P(1
.6,0
,0)
9.5
12.1
12.5
10.0
12.0
14.7
18.5
17.7
21.4
15.3
10.7
8.9
7.7
18.3
18.2
4.8
16.2
11.1
12.1
19.3
13.6
16.8
4.7
16.1
17.4
11.6
9.0
14.3
17.7
12.1
23.3
16.5
23.9
16.3
3.5
GE
P(2
,0.8
,0)
13.5
16.0
11.7
9.6
15.9
14.1
18.4
17.8
23.9
19.7
17.0
14.6
12.3
18.1
18.6
5.0
22.2
14.7
11.6
19.9
14.6
17.9
5.2
18.3
18.6
12.3
7.9
15.2
19.7
14.5
25.7
22.5
32.0
19.4
3.5
GE
P(3
,2.3
,0)
23.4
26.7
10.3
9.1
26.7
12.4
17.0
16.6
28.5
29.7
33.6
30.3
25.7
16.8
19.5
6.5
35.7
23.4
10.6
20.5
18.2
21.3
7.1
23.4
22.1
15.3
5.7
18.6
23.3
20.3
30.6
36.3
47.8
29.7
3.5
GE
P(0
,620
,609
)70
.983
.070
.069
.283
.272
.880
.581
.289
.287
.971
.053
.840
.780
.283
.712
.890
.582
.957
.484
.880
.384
.249
.387
.484
.976
.437
.081
.386
.380
.774
.791
.094
.185
.9
4G
EP
(0.4
,-4.
5,0)
62.5
60.3
33.4
31.9
60.5
27.6
29.3
29.0
20.8
14.1
35.8
61.2
73.4
29.1
29.7
52.8
28.7
40.3
22.5
30.5
43.1
46.0
21.4
21.8
46.3
41.1
18.8
44.5
19.4
15.8
24.0
23.4
3.9
87.4
4G
EP
(0.5
,-3.
2,0)
49.5
47.0
32.0
29.8
47.1
27.8
30.3
29.7
22.4
13.3
25.6
46.6
59.0
30.1
30.0
43.2
21.6
29.7
22.7
30.9
37.7
41.2
17.5
22.6
41.8
35.6
18.9
39.2
20.9
15.0
25.8
18.8
5.1
80.7
4G
EP
(0.6
,-2.
3,0)
34.7
33.5
30.2
27.3
33.6
28.1
31.4
30.6
24.3
12.5
16.6
30.9
40.4
31.2
30.7
32.0
15.7
20.0
22.6
31.8
33.0
37.4
13.9
23.4
38.0
30.6
18.6
34.5
22.5
14.3
28.1
14.8
6.9
68.6
4G
EP
(0.7
,-1.
9,0)
21.0
23.2
28.3
24.6
23.0
28.2
32.2
31.3
26.6
13.6
9.7
16.4
21.5
32.0
31.0
20.2
12.1
13.4
22.4
32.4
28.7
33.7
11.2
24.2
34.5
26.2
18.0
30.3
24.3
15.0
30.6
12.7
10.6
50.5
4G
EP
(0.8
,-1.
5,0)
13.5
18.4
26.9
22.8
18.2
28.4
33.1
31.9
29.3
15.8
6.7
8.6
10.3
32.8
31.7
11.7
13.1
11.5
22.1
33.4
26.6
31.7
9.6
25.6
32.6
23.8
17.4
28.1
26.7
16.3
33.3
13.9
16.2
37.0
4G
EP
(1,-
1.1,
0)11
.218
.125
.921
.417
.928
.934
.333
.333
.820
.97.
65.
85.
334
.033
.16.
919
.414
.422
.135
.125
.831
.28.
728
.532
.222
.616
.527
.330
.419
.237
.120
.026
.430
.1
4G
EP
(1.4
,0,0
)20
.328
.325
.321
.428
.329
.636
.335
.743
.235
.122
.316
.312
.736
.136
.75.
838
.426
.822
.139
.129
.435
.19.
636
.936
.125
.514
.930
.838
.627
.645
.638
.949
.434
.8
4G
EP
(2,1
.5,0
)31
.139
.525
.622
.739
.630
.038
.037
.950
.346
.738
.230
.524
.237
.740
.46.
952
.537
.922
.342
.734
.740
.511
.944
.341
.730
.013
.835
.944
.635
.252
.353
.163
.944
.4
4G
EP
(3,3
.1,0
)44
.654
.127
.126
.054
.330
.539
.940
.458
.660
.356
.947
.438
.239
.645
.710
.166
.751
.522
.947
.743
.048
.716
.953
.849
.937
.611
.944
.051
.945
.960
.667
.876
.757
.2
4G
EP
(0,5
80,5
84)
70.9
83.0
69.8
69.1
83.2
72.6
80.2
81.0
89.1
87.7
71.1
53.7
40.5
80.0
83.6
12.9
90.4
82.9
57.5
84.9
80.1
84.2
49.3
87.4
84.9
76.3
36.7
81.1
86.4
80.7
74.7
91.0
94.0
85.8
4.5
GE
P(0
.4,-
4,0)
48.3
49.1
38.5
35.8
49.4
35.3
39.2
38.5
31.1
16.0
20.4
41.1
54.9
39.0
38.3
44.8
18.8
29.4
28.5
39.8
43.7
48.6
19.5
31.7
49.2
40.8
22.8
45.5
29.7
19.0
34.9
17.9
9.5
83.0
4.5
GE
P(0
.5,-
2.7,
0)35
.938
.537
.433
.938
.736
.140
.739
.833
.417
.213
.427
.338
.040
.439
.534
.816
.022
.828
.641
.140
.245
.717
.033
.346
.537
.122
.542
.032
.219
.937
.716
.612
.874
.5
4.5
GE
P(0
.6,-
2,0)
25.2
30.8
36.8
32.6
30.8
37.4
42.6
41.7
37.0
20.0
8.7
15.2
21.3
42.3
41.2
23.7
16.2
18.1
29.0
43.2
37.9
43.8
15.3
35.4
44.7
34.6
22.3
39.8
35.6
21.9
41.4
17.6
18.2
61.6
4.5
GE
P(0
.7,-
1.5,
0)18
.127
.135
.931
.326
.938
.544
.443
.641
.224
.87.
17.
79.
644
.143
.013
.821
.118
.129
.445
.436
.642
.714
.038
.143
.732
.922
.238
.339
.425
.145
.422
.326
.948
.3
4.5
GE
P(0
.8,-
1.2,
0)17
.128
.036
.031
.127
.839
.846
.245
.646
.231
.39.
46.
15.
545
.945
.28.
529
.622
.329
.847
.837
.043
.413
.941
.844
.533
.021
.838
.843
.729
.149
.330
.538
.242
.8
4.5
GE
P(1
,-0.
8,0)
22.3
34.3
36.8
32.3
34.2
41.7
48.9
48.5
53.2
41.4
18.4
11.2
8.1
48.6
48.8
6.4
43.0
31.7
30.7
51.4
40.1
46.8
14.8
48.0
47.9
35.6
21.6
41.8
49.7
35.7
55.1
43.7
53.4
44.6
4.5
GE
P(1
.3,0
,0)
34.3
46.2
38.6
35.1
46.4
43.6
52.1
52.1
61.5
54.7
35.8
25.2
18.8
51.8
53.7
7.2
59.4
45.5
32.0
56.4
46.1
52.8
17.8
56.4
53.9
41.2
21.2
47.7
57.0
45.0
61.8
60.0
69.4
53.4
4.5
GE
P(2
,2.1
,0)
50.1
62.2
42.2
40.4
62.5
46.6
56.5
57.2
71.0
69.6
57.4
45.4
35.3
56.1
61.0
10.1
74.7
61.2
34.4
63.3
55.8
61.9
24.0
67.1
63.1
50.3
20.8
57.2
66.1
57.1
70.1
75.7
82.9
66.4
4.5
GE
P(3
,3.9
,0)
61.9
73.5
46.4
46.4
73.7
49.6
60.7
61.9
78.2
79.2
71.1
58.2
46.4
60.3
67.4
13.3
83.6
72.1
36.5
69.2
64.6
70.1
30.5
75.3
71.3
59.0
20.1
65.7
72.9
67.0
76.7
84.6
89.7
75.9
4.5
GE
P(0
,550
,557
)70
.983
.069
.869
.283
.172
.680
.381
.089
.187
.771
.153
.740
.580
.183
.612
.990
.582
.757
.584
.980
.284
.349
.387
.384
.976
.336
.881
.186
.280
.674
.391
.094
.185
.8
5G
EP
(0.5
,-2.
4,0)
31.3
39.1
43.4
39.5
39.2
44.4
49.9
49.1
44.4
25.8
8.8
15.7
23.1
49.7
48.4
28.8
20.8
23.9
34.4
50.8
45.7
51.8
19.6
44.0
52.7
41.9
26.2
47.5
43.8
28.3
48.1
22.8
24.1
71.1
5G
EP
(0.6
,-1.
7,0)
24.7
36.3
44.0
39.5
36.3
46.6
52.9
52.3
49.8
32.2
7.8
8.4
11.1
52.6
51.5
18.4
27.3
24.8
35.4
54.1
45.5
51.9
19.3
47.9
53.0
41.5
26.3
47.4
48.9
32.9
52.7
29.2
34.2
60.8
5G
EP
(0.7
,-1.
3,0)
24.0
38.0
44.7
40.1
37.9
48.7
55.6
55.3
56.1
41.0
11.4
6.6
5.9
55.3
55.0
10.7
39.0
30.6
36.7
57.8
46.8
53.4
19.5
52.8
54.5
42.6
26.3
48.7
54.5
38.9
57.6
40.1
48.0
54.1
5G
EP
(0.8
,-1,
0)28
.543
.546
.041
.843
.450
.858
.358
.162
.150
.320
.110
.77.
258
.058
.37.
751
.139
.638
.361
.049
.656
.321
.057
.957
.545
.226
.451
.559
.245
.162
.051
.960
.854
.3
5G
EP
(1,-
0.6,
0)38
.753
.548
.544
.953
.653
.461
.661
.669
.361
.735
.722
.515
.761
.363
.17.
365
.052
.339
.965
.455
.161
.724
.665
.062
.850
.426
.756
.865
.753
.567
.065
.774
.160
.8
5G
EP
(1.1
,0,0
)48
.462
.450
.948
.362
.655
.564
.264
.674
.570
.349
.535
.225
.863
.966
.98.
874
.461
.841
.569
.060
.666
.628
.170
.667
.755
.626
.962
.070
.460
.470
.775
.182
.167
.9
5G
EP
(2,2
.7,0
)64
.676
.857
.256
.477
.160
.470
.171
.083
.182
.470
.055
.743
.469
.875
.013
.086
.376
.245
.576
.571
.276
.337
.480
.677
.366
.427
.472
.479
.072
.577
.187
.191
.479
.8
5G
EP
(3,4
.6,0
)73
.184
.162
.362
.984
.364
.374
.675
.987
.988
.478
.864
.751
.374
.380
.416
.091
.383
.648
.881
.878
.082
.444
.886
.383
.273
.628
.278
.984
.379
.881
.492
.094
.985
.9
5G
EP
(0,5
00,6
00)
71.1
83.0
69.9
69.2
83.2
72.5
80.3
80.9
89.2
87.8
71.2
53.8
40.7
80.1
83.5
13.1
90.5
82.9
57.5
84.8
80.1
84.1
49.5
87.3
84.8
76.2
36.8
81.1
86.2
80.6
74.5
91.1
94.2
85.8
6G
EP
(0.4
,-2.
9,0)
37.6
50.5
54.7
51.2
50.6
56.7
62.8
62.4
58.7
40.2
8.5
11.8
18.4
62.6
61.6
30.3
33.5
35.0
44.3
64.1
57.5
63.8
28.5
59.0
64.7
53.6
32.8
59.5
59.0
42.2
58.6
36.4
39.9
78.0
6G
EP
(0.5
,-1.
9,0)
35.8
51.3
56.5
52.6
51.3
59.6
65.9
65.9
64.5
48.6
10.6
7.6
9.6
65.7
65.3
21.9
43.5
39.3
46.2
67.9
59.3
65.5
29.4
63.9
66.4
55.2
33.0
61.1
64.6
48.5
63.1
45.6
51.6
72.9
6G
EP
(0.6
,-1.
3,0)
38.4
55.5
58.5
54.9
55.5
62.6
69.7
69.6
71.3
59.6
18.7
8.2
6.2
69.4
69.6
13.4
57.8
48.5
48.6
72.0
62.3
68.4
31.6
69.3
69.4
57.9
33.9
64.0
70.2
56.5
67.1
58.8
66.2
69.1
6G
EP
(0.8
,-0.
8,0)
52.6
68.6
63.0
60.6
68.7
67.1
74.6
75.2
81.3
75.7
44.2
25.6
16.4
74.4
76.5
9.5
78.1
67.2
52.3
78.4
70.1
75.5
38.2
78.7
76.4
65.6
34.9
71.4
78.9
68.9
72.3
78.6
84.6
74.7
6G
EP
(1,0
,0)
70.3
82.6
69.1
68.5
82.8
72.2
80.0
80.6
88.8
87.4
70.5
53.3
40.0
79.7
83.2
12.9
90.1
82.6
56.8
84.5
79.7
83.8
48.5
87.0
84.5
75.8
36.5
80.7
85.9
80.2
74.7
90.7
93.9
85.5
6G
EP
(2,3
.9,0
)80
.790
.275
.976
.390
.377
.484
.885
.793
.393
.282
.366
.852
.184
.688
.616
.895
.190
.062
.289
.486
.689
.758
.892
.290
.383
.538
.887
.391
.087
.676
.195
.597
.291
.6
6G
EP
(3,6
.2,0
)84
.292
.479
.380
.292
.580
.387
.388
.394
.995
.085
.470
.055
.087
.190
.918
.696
.392
.364
.991
.789
.492
.063
.594
.192
.486
.840
.390
.092
.990
.376
.496
.798
.093
.4
6G
EP
(0,1
40,1
29.1
)72
.183
.870
.970
.384
.073
.681
.181
.889
.788
.571
.754
.340
.780
.984
.413
.291
.183
.858
.285
.581
.185
.050
.687
.985
.777
.337
.382
.186
.981
.774
.291
.694
.586
.5
10G
EP
(0.4
,-1.
7,0)
73.2
85.7
82.9
82.0
85.8
85.2
89.7
90.1
91.9
88.6
46.1
18.0
9.0
89.6
90.7
21.7
87.9
82.4
72.3
91.7
87.3
90.3
63.8
91.8
90.8
84.8
50.0
88.1
91.6
86.0
65.6
88.4
91.6
90.8
10G
EP
(0.5
,-1,
0)83
.191
.987
.086
.892
.088
.492
.592
.995
.794
.670
.841
.323
.592
.493
.918
.595
.191
.276
.794
.591
.893
.872
.195
.394
.189
.852
.392
.394
.991
.962
.495
.397
.093
.8
10G
EP
(0.7
,0,0
)96
.999
.094
.294
.999
.093
.796
.597
.099
.299
.396
.889
.077
.596
.598
.129
.599
.698
.985
.098
.398
.098
.688
.999
.198
.797
.457
.898
.298
.798
.249
.299
.799
.899
.1
10G
EP
(1.4
,5.7
,0)
92.2
96.8
90.9
91.3
96.9
91.4
94.9
95.3
98.1
98.0
89.9
74.2
58.1
94.8
96.5
21.3
98.6
96.8
80.8
96.7
95.7
96.9
81.1
97.8
97.1
94.4
54.9
96.0
97.2
96.0
56.4
98.7
99.3
97.4
10G
EP
(0,6
,12.
2)88
.895
.087
.687
.995
.188
.592
.993
.397
.096
.786
.068
.652
.892
.794
.818
.497
.795
.076
.895
.293
.595
.275
.396
.595
.591
.851
.594
.095
.894
.060
.497
.998
.795
.9
10G
EP
(0,1
7,-1
2.6)
89.0
95.3
88.1
88.5
95.4
88.9
93.1
93.6
97.3
97.0
86.4
69.1
53.1
93.0
95.0
18.8
97.7
95.3
77.5
95.5
93.8
95.4
76.1
96.7
95.7
92.2
52.0
94.2
96.1
94.3
60.1
98.0
98.8
96.1
20G
EP
(0.3
,-1.
3,0)
97.3
99.1
97.1
97.4
99.1
97.1
98.5
98.7
99.5
99.5
93.3
71.7
46.8
98.5
99.1
31.3
99.5
99.0
91.8
99.1
98.8
99.2
93.1
99.4
99.2
98.4
66.9
98.9
99.2
98.9
36.4
99.6
99.7
99.2
20G
EP
(0.5
,0,0
)99
.910
099
.699
.710
099
.299
.799
.810
010
099
.999
.296
.699
.799
.955
.010
010
097
.199
.999
.910
099
.310
010
099
.974
.410
099
.999
.914
.310
010
010
0
20G
EP
(0.8
,2.3
,0)
99.4
99.8
98.8
99.0
99.8
98.6
99.3
99.4
99.9
99.9
98.8
93.0
81.7
99.3
99.7
38.2
99.9
99.8
95.0
99.7
99.7
99.8
97.4
99.9
99.8
99.6
71.2
99.7
99.8
99.7
24.5
100
100
99.8
20G
EP
(0,1
4,-1
7.6)
96.8
98.9
95.9
96.3
98.9
95.9
97.8
98.0
99.3
99.3
95.0
82.1
66.0
97.7
98.6
26.3
99.5
98.9
89.2
98.7
98.4
98.8
90.9
99.2
98.9
97.8
63.8
98.5
98.9
98.6
40.3
99.6
99.8
99.1
20G
EP
(0,6
,2.6
)95
.098
.294
.294
.598
.294
.396
.897
.199
.098
.992
.778
.161
.796
.797
.923
.699
.298
.286
.498
.197
.598
.287
.498
.898
.396
.660
.597
.798
.497
.746
.099
.399
.698
.5
50G
EP
(0.3
,-0.
7,0)
100
100
99.9
99.9
100
99.8
99.9
99.9
100
100
100
99.2
95.8
99.9
100
60.5
100
100
99.0
100
100
100
99.8
100
100
100
80.6
100
100
100
6.1
100
100
100
50G
EP
(0.4
,0,0
)10
010
010
010
010
099
.910
010
010
010
010
010
099
.810
010
078
.410
010
099
.710
010
010
010
010
010
010
084
.510
010
010
01.
610
010
010
0
50G
EP
(0.6
,1.2
,0)
100
100
100
100
100
99.9
100
100
100
100
100
99.8
98.3
100
100
68.7
100
100
99.5
100
100
100
99.9
100
100
100
83.8
100
100
100
2.8
100
100
100
50G
EP
(0,5
.1,2
.1)
96.9
99.0
96.3
96.6
99.0
96.3
98.0
98.2
99.4
99.4
95.1
82.4
66.3
98.0
98.8
26.6
99.6
99.0
90.1
98.9
98.5
99.0
91.7
99.3
99.0
98.0
64.7
98.7
99.1
98.7
37.7
99.6
99.8
99.2
50G
EP
(0,8
,-7.
2)98
.899
.698
.298
.499
.698
.099
.099
.199
.899
.897
.788
.674
.199
.099
.532
.399
.999
.694
.199
.599
.499
.695
.899
.799
.699
.170
.299
.499
.699
.527
.299
.999
.999
.7
50G
EP
(0,1
0,-1
3.8)
99.5
99.9
99.1
99.3
99.9
98.9
99.5
99.6
99.9
99.9
99.0
93.2
80.9
99.5
99.8
38.6
100
99.9
96.3
99.8
99.8
99.8
98.0
99.9
99.9
99.7
74.0
99.8
99.8
99.8
19.2
100
100
99.9
50G
EP
(0,1
0.8,
-17.
3)99
.810
099
.699
.710
099
.599
.899
.810
010
099
.696
.587
.799
.899
.946
.510
010
097
.899
.999
.999
.999
.110
010
099
.977
.099
.999
.999
.912
.910
010
010
0
Mea
n
100
62.4
68.1
59.4
58.5
68.1
54.5
51.1
57.3
43.6
63.5
60.0
56.5
52.9
50.6
58.3
36.7
69.0
64.4
36.0
62.5
65.3
64.2
56.3
49.3
63.9
64.8
35.4
65.2
61.7
60.6
24.2
67.3
49.2
73.5
Ran
k
100
143.
518
193.
524
2621
3012
1722
2527
2031
29
3213
610
2328
118
337
1516
345
291
Dev
.to
the
Bes
t-
Mea
n
100
16.6
10.9
19.5
20.5
10.9
24.4
27.9
21.7
35.4
15.5
19.0
22.4
26.1
28.4
20.6
42.3
10.0
14.6
43.0
16.4
13.7
14.8
22.6
29.7
15.1
14.2
43.6
13.8
17.2
18.4
54.8
11.7
29.8
5.5
Ran
k
100
143.
518
193.
524
2621
3012
1722
2527
2031
29
3213
610
2328
118
337
1516
345
291
Dev
.to
the
Bes
t-
Max
100
74.5
44.3
62.6
62.4
44.5
99.2
89.0
79.1
99.5
73.3
77.4
88.9
91.9
89.6
76.2
83.6
64.2
59.5
93.9
71.6
46.7
50.8
66.0
99.8
52.8
47.7
87.5
45.7
82.7
72.3
100
65.1
97.8
40.0
Ran
k
100
182
1110
331
2621
3217
2025
2827
1923
129
2915
57
1433
86
244
2216
3413
301
35
Tab
le6:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=20
0(b
egin
nin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
1.1
GE
P(1
,-40
.5,0
)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
095
.810
010
099
.610
010
010
010
010
010
010
010
010
010
010
00.
599
.910
010
0
1.1
GE
P(4
,-18
.1,0
)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
098
.110
010
010
010
010
010
010
010
010
010
010
010
010
010
00.
399
.910
010
0
1.1
GE
P(6
,-14
.6,0
)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
099
.110
010
010
010
010
010
010
010
010
010
010
010
010
010
00.
310
010
010
0
1.1
GE
P(8
,-12
.9,0
)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
099
.610
010
010
010
010
010
010
010
010
010
010
010
010
010
00.
210
010
010
0
1.1
GE
P(1
5,-1
0.9,
0)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
00.
210
010
010
0
1.1
GE
P(3
0,-1
0,0)
100
100
100
100
100
0.0
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
0.2
100
100
100
1.1
GE
P(6
0,-9
.8,0
)10
010
010
010
010
00.
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
00.
210
010
010
0
1.5
GE
P(1
,-8.
3,0)
100
100
100
100
100
43.0
100
100
100
100
100
100
100
100
100
95.0
100
100
99.9
100
100
100
100
0.1
100
100
71.1
100
100
100
0.0
100
69.9
100
1.5
GE
P(2
,-5.
7,0)
100
100
100
100
100
45.0
100
100
100
100
100
100
100
100
100
94.2
100
100
100
100
100
100
100
0.4
100
100
86.3
100
100
100
0.0
100
89.0
100
1.5
GE
P(4
,-3.
7,0)
100
100
100
100
100
46.8
100
100
100
100
100
100
100
100
100
94.3
100
100
100
100
100
100
100
31.9
100
100
98.2
100
100
100
0.0
100
99.6
100
1.5
GE
P(6
,-2.
9,0)
100
100
100
100
100
47.8
100
100
100
100
100
100
100
100
100
96.8
100
100
100
100
100
100
100
59.7
100
100
99.9
100
100
100
0.0
100
100
100
1.5
GE
P(8
,-2.
5,0)
100
100
100
100
100
48.0
100
100
100
100
100
100
100
100
100
97.8
100
100
100
100
100
100
100
70.6
100
100
100
100
100
100
0.0
100
100
100
1.5
GE
P(1
5,-2
.1,0
)10
010
010
010
010
048
.410
010
010
010
010
010
010
010
010
098
.610
010
010
010
010
010
010
080
.810
010
010
010
010
010
00.
010
010
010
0
1.5
GE
P(3
0,-1
.9,0
)10
010
010
010
010
048
.810
010
010
010
010
010
099
.910
010
098
.710
010
010
010
010
010
010
083
.210
010
010
010
010
010
00.
010
010
010
0
1.5
GE
P(6
0,-1
.8,0
)10
010
010
010
010
048
.510
010
010
010
010
010
099
.910
010
098
.610
010
010
010
010
010
010
083
.910
010
010
010
010
010
00.
010
010
010
0
1.84
GE
P(0
.6,-
8.4,
0)10
010
010
010
010
098
.997
.598
.499
.310
010
010
010
097
.210
094
.510
010
083
.510
010
010
010
00.
110
010
032
.510
099
.110
00.
099
.910
.610
0
1.84
GE
P(0
.8,-
6,0)
100
100
100
100
100
99.3
98.0
98.8
99.4
100
100
100
100
97.9
100
94.2
100
100
83.6
100
100
100
100
1.1
100
100
34.1
100
99.4
100
0.0
100
11.4
100
1.84
GE
P(1
,-5,
0)10
010
010
010
010
099
.698
.699
.299
.610
010
010
010
098
.410
092
.810
010
083
.910
010
010
010
07.
110
010
036
.910
099
.610
00.
010
012
.510
0
1.84
GE
P(1
.5,-
3.9,
0)10
010
010
010
010
099
.999
.499
.799
.810
010
010
010
099
.310
081
.510
010
082
.310
010
010
010
058
.910
010
044
.810
099
.910
00.
010
017
.310
0
1.84
GE
P(2
,-3.
2,0)
100
100
100
100
100
100
99.7
99.9
99.9
100
100
100
100
99.7
100
71.7
100
100
80.0
100
100
100
100
89.8
100
100
52.9
100
100
100
0.0
100
23.8
100
1.84
GE
P(3
,-2.
1,0)
99.9
100
100
100
100
100
99.9
100
99.7
100
100
99.9
99.6
99.9
100
65.4
100
100
76.7
100
100
100
100
99.0
100
100
66.9
100
100
100
0.0
100
39.0
100
1.84
GE
P(4
,-1.
4,0)
99.4
100
100
100
100
100
100
100
99.5
100
99.9
98.8
95.5
100
100
63.6
100
100
74.2
100
100
100
100
99.7
100
100
78.6
100
100
100
0.0
100
55.6
100
1.84
GE
P(6
,-0.
7,0)
97.4
100
100
100
100
100
100
100
98.8
100
98.7
90.3
75.8
100
100
60.8
100
99.8
71.0
100
100
100
100
99.9
99.9
100
91.8
100
100
100
0.0
100
80.5
100
1.84
GE
P(8
,-0.
4,0)
95.5
100
100
100
100
100
100
100
98.2
100
96.7
79.8
58.7
100
100
58.2
100
99.5
69.4
100
100
100
100
100
100
100
97.0
100
100
100
0.0
100
92.7
100
1.84
GE
P(1
5.2,
0,0)
91.7
99.9
100
100
99.9
100
100
100
97.0
100
90.3
59.2
35.7
100
100
50.8
99.9
98.7
66.5
100
100
100
100
100
100
100
99.9
100
100
99.9
0.0
99.9
99.6
99.9
2G
EP
(0.5
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9,0)
100
100
100
100
100
95.5
89.0
92.6
95.6
100
100
100
100
88.2
99.5
94.4
100
100
65.5
99.5
100
100
100
0.7
100
100
23.7
100
93.9
100
0.0
99.9
3.8
100
2G
EP
(0.8
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1,0)
100
100
100
100
100
96.5
89.9
93.5
95.8
100
100
100
100
89.0
99.3
93.0
100
100
63.0
99.4
100
100
100
6.8
100
100
24.6
100
95.3
100
0.0
99.9
4.0
100
2G
EP
(1,-
4.2,
0)10
010
099
.999
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097
.390
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010
010
010
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099
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410
0
2G
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2,0)
100
100
99.4
99.1
100
98.6
92.6
95.9
95.3
100
100
100
100
91.7
98.6
68.0
100
100
53.4
99.5
100
100
99.9
76.2
100
100
32.0
100
98.4
100
0.0
100
5.9
100
2G
EP
(2,-
2.5,
0)99
.710
098
.798
.210
099
.393
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010
099
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010
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010
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910
0
2G
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(3,-
1.4,
0)94
.999
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099
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2G
EP
(4,-
0.7,
0)86
.698
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099
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2G
EP
(6,0
,0)
72.8
96.7
99.6
99.6
96.9
99.9
96.1
98.5
71.5
98.9
76.4
47.0
29.1
95.2
96.7
33.4
98.2
90.9
31.4
99.6
99.3
96.5
99.9
99.8
95.3
99.7
77.6
99.0
100
97.6
0.0
98.2
42.1
97.0
2G
EP
(8,0
.3,0
)64
.895
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096
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2G
EP
(15,
0.7,
0)55
.195
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095
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895
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092
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2G
EP
(0,8
65,8
73)
94.3
98.4
92.5
92.6
98.5
93.6
96.6
96.8
99.2
99.1
94.1
82.0
67.5
96.4
97.9
24.8
99.6
98.7
79.6
98.3
97.6
98.3
84.1
99.1
98.4
96.5
49.3
97.7
98.6
97.8
88.4
99.6
99.8
98.8
2.25
GE
P(0
.5,-
7.2,
0)10
010
099
.699
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080
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410
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299
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810
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2.25
GE
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.7,-
4.7,
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010
098
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080
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010
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010
034
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110
010
015
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074
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199
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710
0
2.25
GE
P(0
.8,-
3.8,
0)10
010
096
.495
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080
.158
.368
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010
010
056
.285
.386
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010
030
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099
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016
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.699
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199
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710
0
2.25
GE
P(1
,-3.
3,0)
100
100
92.6
91.4
100
80.3
56.6
67.8
67.3
99.1
100
100
100
54.3
81.9
76.2
100
100
26.8
89.0
99.8
99.6
98.7
32.9
99.6
99.8
16.0
99.8
76.0
98.5
0.0
99.6
0.7
100
2.25
GE
P(1
.5,-
2.4,
0)96
.898
.977
.875
.999
.081
.051
.264
.450
.296
.699
.199
.098
.548
.570
.743
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.798
.617
.584
.493
.488
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.067
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.394
.318
.292
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.893
.20.
099
.10.
899
.1
2.25
GE
P(2
,-1.
7,0)
81.6
91.8
69.7
68.7
92.2
81.6
47.5
61.8
35.8
92.2
92.0
87.8
82.6
44.5
62.6
29.6
98.2
91.8
12.6
80.7
82.3
71.4
86.2
80.5
68.5
85.4
20.6
80.7
82.1
85.5
0.0
97.4
1.0
91.8
2.25
GE
P(3
,-0.
5,0)
48.1
70.7
66.5
66.9
71.6
82.4
43.1
58.6
18.9
81.3
60.4
43.6
32.4
39.7
52.5
19.3
87.8
68.4
7.9
76.2
69.3
51.3
82.7
87.7
47.3
74.9
26.3
66.0
85.4
71.1
0.0
87.3
1.6
69.8
2.25
GE
P(3
.7,0
,0)
35.4
61.0
68.5
69.3
61.9
82.9
41.4
57.6
13.6
74.5
42.2
25.1
16.6
37.9
48.6
16.1
78.9
55.3
6.6
74.7
66.6
46.4
83.9
88.6
42.1
73.4
30.5
62.7
87.3
64.0
0.0
78.8
2.1
61.5
2.25
GE
P(4
,0.2
,0)
30.5
56.9
70.0
71.3
57.8
83.1
40.4
56.9
11.8
71.1
34.9
19.0
12.2
37.0
46.8
14.7
74.1
49.1
6.1
74.0
66.2
44.8
85.2
88.5
40.3
73.5
32.6
61.9
88.1
60.6
0.0
74.1
2.4
58.5
2.25
GE
P(8
,1.2
,0)
13.7
43.1
86.7
88.4
43.7
83.4
36.4
53.6
4.6
50.4
8.2
4.4
5.0
32.9
37.1
7.8
43.3
22.5
3.8
70.0
76.2
48.6
95.7
85.3
42.8
83.9
56.3
70.5
92.8
42.6
0.0
44.0
9.7
53.4
2.25
GE
P(0
,785
,782
)94
.598
.592
.792
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.996
.796
.999
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.194
.282
.067
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.697
.925
.099
.698
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.384
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.496
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2.5
GE
P(0
.5,-
6.1,
0)10
010
094
.093
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058
.036
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010
010
034
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099
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510
010
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098
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210
0
2.5
GE
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3.9,
0)10
010
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054
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010
010
029
.060
.386
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.068
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797
.90.
110
0
2.5
GE
P(0
.8,-
3.2,
0)99
.910
072
.571
.510
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.126
.737
.733
.189
.999
.810
010
024
.851
.975
.599
.599
.614
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.797
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.712
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.60.
597
.40.
199
.9
2.5
GE
P(1
,-2.
7,0)
98.8
99.3
58.7
58.0
99.3
47.7
22.4
33.3
24.8
85.1
99.0
99.7
99.8
20.7
42.8
58.6
98.8
97.7
11.3
56.1
90.4
86.8
80.5
25.4
85.6
90.5
11.2
90.2
42.6
78.6
0.3
96.4
0.1
99.6
2.5
GE
P(1
.5,-
1.8,
0)66
.273
.432
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.074
.140
.213
.924
.08.
864
.378
.278
.576
.012
.423
.924
.287
.371
.25.
939
.851
.040
.052
.740
.637
.454
.410
.349
.340
.351
.90.
184
.80.
177
.2
2.5
GE
P(2
,-1,
0)34
.743
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.627
.244
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.019
.13.
747
.245
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.134
.58.
815
.614
.166
.042
.93.
931
.231
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.342
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.118
.336
.210
.729
.439
.135
.40.
064
.90.
141
.9
2.5
GE
P(2
.8,0
,0)
14.1
22.2
21.4
24.5
22.8
32.0
6.7
14.7
1.2
29.6
17.3
11.8
9.1
5.7
9.5
8.9
38.3
20.5
2.5
23.9
21.3
10.6
37.7
43.2
9.0
26.4
12.0
18.8
38.4
22.0
0.0
38.4
0.1
20.1
2.5
GE
P(3
,0.2
,0)
11.6
18.8
21.1
24.4
19.2
31.0
6.1
13.7
1.0
26.2
13.3
8.7
6.8
5.1
8.4
8.0
32.9
16.9
2.2
22.6
19.8
9.4
37.6
42.4
7.9
25.2
12.3
17.3
38.4
19.3
0.0
33.1
0.2
17.7
2.5
GE
P(4
,0.9
,0)
6.5
12.1
22.9
26.4
12.4
27.9
4.3
11.0
0.3
16.0
5.3
4.7
5.1
3.6
5.5
5.8
16.9
9.0
1.6
18.1
18.1
7.1
41.2
37.8
5.7
24.1
14.5
15.0
38.0
12.6
0.0
17.2
0.3
15.4
2.5
GE
P(8
,1.9
,0)
6.4
12.1
39.7
43.4
12.3
24.1
2.6
7.4
0.1
6.0
7.5
14.7
17.7
2.1
2.9
4.1
4.8
4.5
0.9
12.9
28.8
9.5
66.5
27.9
7.4
38.2
24.3
22.7
41.8
6.5
0.0
5.0
1.8
28.7
2.5
GE
P(0
,730
,739
)94
.498
.492
.692
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.796
.796
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.382
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.679
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.099
.198
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.299
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2.75
GE
P(0
.5,-
5.3,
0)10
010
077
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899
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894
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110
0
2.75
GE
P(0
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4.1,
0)10
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693
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2.75
GE
P(0
.7,-
3.3,
0)99
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010
015
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491
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099
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2.75
GE
P(0
.8,-
2.8,
0)98
.999
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.020
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189
.40.
099
.6
2.75
GE
P(1
,-2.
3,0)
83.8
84.9
28.8
29.3
85.5
22.6
9.7
15.1
6.5
49.7
85.7
92.8
94.3
8.9
19.1
40.4
84.5
75.8
8.0
25.2
56.3
51.1
42.8
14.7
49.5
56.5
9.5
56.1
18.4
39.8
1.6
79.2
0.0
94.4
2.75
GE
P(1
.5,-
1.4,
0)26
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68.
12.
022
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27.
512
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711
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316
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940
.60.
131
.4
2.75
GE
P(2
,-0.
5,0)
9.9
10.8
7.3
9.4
11.1
9.2
2.6
5.2
1.2
11.8
11.5
10.4
9.3
2.4
3.6
7.2
18.2
10.2
3.3
6.4
8.1
4.9
13.4
13.5
4.4
9.7
6.2
7.3
10.9
8.9
0.6
18.2
0.3
8.8
2.75
GE
P(2
.3,0
,0)
6.4
7.3
6.2
8.4
7.5
7.6
2.0
4.2
1.0
8.5
6.8
6.1
5.6
1.7
2.4
5.8
11.5
7.1
2.8
4.8
6.4
3.5
12.5
12.0
3.1
7.9
5.9
5.5
9.9
6.9
0.5
11.6
0.6
5.6
2.75
GE
P(3
,0.8
,0)
4.7
5.0
5.3
7.5
5.0
5.4
1.1
2.7
0.9
4.7
4.6
5.6
6.0
1.0
1.2
4.6
5.0
4.7
2.1
2.9
4.9
2.2
12.6
8.9
1.9
6.5
5.6
4.1
8.2
4.7
0.4
5.1
2.0
5.6
2.75
GE
P(4
,1.6
,0)
6.8
6.4
5.7
7.7
6.5
3.9
0.7
1.9
0.7
3.3
8.7
12.5
13.8
0.6
0.7
4.3
3.8
4.4
1.7
1.8
5.6
2.2
16.0
6.3
1.9
7.5
5.7
4.4
7.2
4.0
0.4
3.9
5.0
11.7
2.75
GE
P(0
,690
,706
)94
.498
.392
.692
.798
.493
.796
.796
.999
.199
.194
.182
.267
.596
.597
.924
.899
.698
.779
.698
.397
.698
.284
.199
.098
.396
.549
.597
.798
.597
.888
.299
.699
.898
.8
3G
EP
(0.5
,-4.
6,0)
100
100
59.9
60.8
100
26.9
18.4
22.4
14.5
59.3
99.1
100
100
17.6
34.8
86.6
93.9
98.0
15.7
36.6
96.6
96.1
76.9
9.0
95.7
95.9
14.8
96.8
15.2
56.7
6.6
85.3
0.0
99.9
3G
EP
(0.6
,-3.
6,0)
99.7
99.8
50.0
50.6
99.8
24.2
16.6
20.0
11.8
52.2
97.5
99.8
100
15.8
30.2
81.0
91.0
95.7
14.2
31.7
90.9
89.9
65.6
8.8
89.2
89.7
14.1
91.3
14.0
47.8
6.5
82.0
0.0
99.8
3G
EP
(0.7
,-2.
9,0)
97.9
98.0
39.9
39.9
98.2
21.3
15.0
17.8
9.5
43.6
93.3
98.9
99.6
14.3
25.7
70.2
85.4
89.4
12.8
26.7
78.8
77.2
51.0
8.9
76.3
76.9
13.1
79.3
12.5
38.0
6.3
76.4
0.0
99.4
3G
EP
(0.8
,-2.
5,0)
89.6
89.5
30.7
30.4
90.1
18.6
13.3
15.7
7.5
35.4
84.3
94.9
97.4
12.7
21.2
54.6
76.1
75.4
11.8
22.0
60.8
59.0
37.0
9.2
58.0
58.9
11.9
61.4
11.1
29.0
6.2
68.1
0.0
97.8
3G
EP
(1,-
1.9,
0)51
.147
.918
.517
.548
.813
.610
.711
.95.
620
.251
.565
.770
.810
.214
.925
.747
.436
.59.
414
.728
.627
.817
.78.
727
.427
.610
.129
.18.
815
.25.
743
.60.
172
.9
3G
EP
(1.5
,-1,
0)9.
48.
68.
37.
78.
77.
67.
07.
25.
07.
29.
811
.111
.36.
77.
97.
710
.37.
36.
57.
48.
48.
46.
56.
48.
48.
17.
08.
46.
06.
25.
110
.21.
411
.6
3G
EP
(2,0
,0)
5.0
5.0
5.2
5.2
5.0
5.1
5.2
5.1
5.2
5.1
4.9
5.0
4.8
5.0
5.2
5.0
4.9
5.1
5.2
5.0
5.2
5.1
5.1
4.9
5.2
5.0
5.1
5.1
4.9
5.0
5.1
5.0
4.9
4.8
36
Tab
le6:
Pow
erag
ainst
GE
Pdis
trib
uti
onfo
r5%
leve
lte
sts.M
=10
0,00
0.n
=20
0(c
onti
nuin
g)
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3G
EP
(3,1
.4,0
)9.
99.
03.
03.
69.
22.
53.
02.
75.
67.
414
.115
.815
.32.
72.
94.
59.
97.
23.
62.
95.
24.
36.
54.
44.
25.
03.
14.
74.
05.
75.
110
.116
.611
.5
3G
EP
(0,6
65,6
61)
94.5
98.4
92.8
92.8
98.5
93.9
96.7
96.9
99.1
99.1
94.3
82.0
67.7
96.6
97.9
24.8
99.6
98.7
79.7
98.3
97.7
98.3
84.1
99.1
98.4
96.6
49.5
97.8
98.6
97.9
88.2
99.6
99.8
98.9
3.5
GE
P(0
.5,-
3.8,
0)97
.597
.945
.444
.698
.027
.328
.328
.116
.623
.484
.597
.899
.427
.734
.578
.263
.782
.620
.932
.878
.779
.441
.419
.379
.175
.219
.479
.717
.022
.520
.452
.60.
599
.5
3.5
GE
P(0
.6,-
2.8,
0)90
.090
.339
.037
.090
.826
.128
.027
.516
.617
.770
.992
.397
.227
.532
.567
.651
.068
.020
.030
.964
.166
.129
.018
.865
.959
.918
.565
.517
.117
.021
.442
.20.
698
.6
3.5
GE
P(0
.7,-
2.3,
0)70
.069
.033
.530
.070
.025
.428
.127
.117
.212
.950
.877
.087
.127
.530
.749
.434
.844
.519
.229
.747
.951
.318
.918
.451
.543
.317
.549
.417
.712
.922
.929
.61.
095
.0
3.5
GE
P(0
.8,-
1.9,
0)42
.340
.228
.623
.941
.224
.227
.726
.518
.310
.129
.550
.662
.127
.229
.030
.319
.823
.018
.228
.734
.539
.111
.918
.239
.630
.216
.436
.218
.810
.624
.417
.92.
280
.0
3.5
GE
P(1
,-1.
4,0)
12.6
14.5
22.7
17.4
14.7
23.0
27.5
26.1
22.0
9.7
8.4
13.1
16.5
27.0
27.0
11.0
8.4
8.6
16.5
28.1
22.8
27.6
6.5
19.0
28.3
19.1
14.2
24.2
21.2
10.4
27.7
8.7
8.1
37.3
3.5
GE
P(1
.6,0
,0)
13.2
18.3
17.3
12.6
18.6
21.0
27.0
25.6
32.1
23.4
14.8
11.1
9.0
26.4
26.2
5.4
26.7
17.3
14.5
29.2
20.5
24.9
5.8
26.9
25.6
16.6
10.3
21.4
27.8
17.7
35.8
27.2
37.3
24.3
3.5
GE
P(2
,0.8
,0)
21.4
26.9
16.1
12.1
27.4
20.2
27.0
25.5
36.7
32.4
27.3
22.1
18.1
26.2
27.2
6.1
39.1
26.0
14.0
30.3
23.4
27.5
7.4
31.7
28.2
19.0
8.5
24.1
30.9
23.1
39.7
39.8
51.5
31.1
3.5
GE
P(3
,2.3
,0)
42.0
48.9
14.6
12.8
49.7
17.5
25.2
23.9
45.7
51.7
57.0
51.1
43.6
24.4
30.3
9.9
62.7
46.2
13.4
33.0
33.2
35.8
14.5
42.2
36.5
28.1
5.0
33.2
36.2
36.2
47.2
63.5
74.3
52.7
3.5
GE
P(0
,620
,609
)94
.598
.492
.992
.898
.593
.996
.897
.099
.299
.194
.382
.367
.896
.797
.925
.099
.598
.779
.998
.397
.798
.384
.299
.198
.496
.649
.497
.898
.697
.988
.199
.699
.898
.9
4G
EP
(0.4
,-4.
5,0)
94.2
95.6
52.0
50.0
96.0
38.8
42.8
41.7
28.4
15.1
67.5
93.5
98.3
42.3
45.5
77.8
39.9
72.0
28.9
45.1
76.1
78.7
35.6
34.5
78.7
71.6
25.8
77.4
31.0
19.2
36.1
32.2
2.5
99.3
4G
EP
(0.5
,-3.
2,0)
83.3
86.0
48.8
45.4
86.7
39.7
44.5
43.2
30.6
13.5
50.3
83.1
93.2
43.9
45.7
68.1
28.4
57.0
28.9
46.0
66.0
70.0
27.6
35.7
70.3
60.6
25.1
67.7
33.5
18.0
39.2
23.8
3.6
98.4
4G
EP
(0.6
,-2.
3,0)
62.4
66.1
45.5
40.7
67.3
40.6
45.9
44.4
33.4
13.3
30.9
61.9
78.4
45.3
45.7
52.8
18.3
38.0
28.7
47.2
55.5
61.1
20.9
37.2
61.6
50.0
24.3
57.4
36.6
17.8
42.8
16.8
6.0
95.6
4G
EP
(0.7
,-1.
9,0)
35.9
42.1
42.4
36.4
43.0
41.3
47.4
46.0
37.3
15.4
15.0
33.2
47.4
46.8
46.3
32.2
12.8
21.4
28.2
48.6
47.0
53.3
15.9
38.9
54.1
41.4
23.7
48.9
40.1
19.3
46.7
13.5
11.2
83.8
4G
EP
(0.8
,-1.
5,0)
19.8
29.3
40.3
33.3
29.7
42.4
49.0
47.7
42.2
20.4
7.4
13.0
19.2
48.4
47.3
16.8
15.9
15.9
28.0
50.6
42.1
48.8
13.4
41.8
49.8
36.5
22.9
44.0
44.1
22.6
51.1
17.1
20.9
63.2
4G
EP
(1,-
1.1,
0)15
.628
.238
.731
.428
.443
.451
.249
.950
.130
.98.
45.
96.
050
.549
.38.
629
.921
.828
.153
.640
.947
.712
.647
.648
.735
.121
.742
.750
.029
.157
.330
.739
.548
.3
4G
EP
(1.4
,0,0
)34
.748
.539
.233
.549
.146
.155
.654
.665
.257
.336
.624
.718
.454
.856
.07.
864
.048
.829
.260
.549
.255
.417
.362
.056
.442
.518
.850
.561
.246
.868
.864
.774
.256
.3
4G
EP
(2,1
.5,0
)55
.267
.941
.938
.268
.648
.059
.058
.475
.174
.364
.151
.641
.558
.163
.011
.481
.768
.631
.266
.860
.465
.426
.172
.766
.353
.716
.361
.369
.061
.676
.982
.388
.672
.1
4G
EP
(3,3
.1,0
)74
.384
.647
.046
.285
.050
.363
.263
.184
.387
.784
.975
.464
.562
.371
.618
.492
.784
.234
.474
.573
.677
.040
.783
.477
.667
.913
.274
.077
.276
.485
.093
.396
.286
.4
4G
EP
(0,5
80,5
84)
94.4
98.4
92.7
92.8
98.5
93.8
96.8
96.9
99.1
99.1
94.4
82.2
67.7
96.6
98.0
25.1
99.6
98.7
80.1
98.3
97.7
98.3
84.4
99.1
98.4
96.7
49.9
97.8
98.6
97.9
88.0
99.6
99.8
98.9
4.5
GE
P(0
.4,-
4,0)
81.6
87.0
58.5
55.1
87.8
51.8
57.4
56.0
43.6
17.5
38.6
76.7
91.0
56.9
57.0
70.9
21.3
56.4
37.2
58.8
72.4
76.6
32.8
50.7
77.0
67.2
30.9
74.0
48.5
25.5
52.6
19.9
9.1
98.7
4.5
GE
P(0
.5,-
2.7,
0)64
.372
.956
.952
.274
.053
.559
.658
.447
.620
.522
.654
.874
.959
.158
.358
.617
.242
.837
.661
.166
.271
.628
.353
.672
.160
.730
.767
.953
.028
.057
.018
.213
.997
.1
4.5
GE
P(0
.6,-
2,0)
43.2
55.8
55.6
49.8
56.9
55.7
62.3
61.2
53.1
26.4
11.3
28.6
45.7
61.7
60.5
41.0
19.2
31.5
38.2
64.0
61.1
67.3
24.7
57.0
68.0
55.3
30.8
63.0
57.7
32.2
62.1
21.4
22.8
91.5
4.5
GE
P(0
.7,-
1.5,
0)28
.745
.755
.048
.646
.358
.365
.564
.560
.236
.57.
210
.416
.764
.963
.521
.530
.428
.539
.067
.658
.665
.023
.261
.865
.952
.630
.060
.463
.539
.267
.632
.238
.677
.9
4.5
GE
P(0
.8,-
1.2,
0)27
.646
.555
.348
.746
.960
.368
.267
.567
.549
.111
.46.
26.
367
.666
.612
.247
.437
.740
.271
.059
.365
.823
.767
.266
.653
.229
.561
.068
.747
.472
.748
.657
.568
.0
4.5
GE
P(1
,-0.
8,0)
37.9
56.9
56.9
51.1
57.4
63.2
71.5
71.0
76.2
65.1
29.0
14.9
9.5
70.9
71.2
8.9
68.8
55.4
42.2
75.3
63.9
69.8
27.5
74.8
70.7
57.8
28.8
65.3
75.1
58.9
78.4
69.5
77.5
68.6
4.5
GE
P(1
.3,0
,0)
58.7
74.9
61.1
57.3
75.5
67.2
76.3
76.1
85.6
81.8
60.2
42.3
31.0
75.6
78.2
11.2
86.7
76.2
45.5
81.5
73.9
78.4
36.7
84.2
79.2
68.0
28.1
74.8
82.7
73.2
85.2
87.1
91.8
80.3
4.5
GE
P(2
,2.1
,0)
79.9
90.0
68.2
67.1
90.4
72.1
81.5
81.7
92.8
93.1
85.5
72.9
60.2
80.9
85.9
18.5
96.0
90.7
51.1
88.0
85.2
88.0
52.9
92.2
88.4
80.8
26.2
85.7
89.4
86.4
91.4
96.3
98.0
91.9
4.5
GE
P(3
,3.9
,0)
90.0
96.0
75.3
76.0
96.2
76.5
86.0
86.4
96.4
97.3
94.4
86.2
75.0
85.5
91.4
26.0
98.7
96.3
56.0
92.5
92.1
93.7
67.0
96.3
94.0
89.2
24.3
92.4
93.6
93.3
95.3
98.8
99.4
96.7
4.5
GE
P(0
,550
,557
)94
.498
.392
.792
.798
.493
.996
.896
.999
.199
.194
.382
.267
.796
.697
.925
.099
.698
.779
.798
.397
.698
.384
.299
.198
.496
.549
.897
.798
.697
.888
.299
.699
.898
.8
5G
EP
(0.5
,-2.
4,0)
53.1
68.8
65.5
60.8
69.7
65.6
72.0
71.2
63.5
36.3
10.6
29.4
49.6
71.5
70.1
50.5
26.9
42.9
46.2
73.8
71.7
76.9
34.9
68.9
77.6
66.3
36.3
73.3
69.2
43.4
69.9
30.1
32.4
95.9
5G
EP
(0.6
,-1.
7,0)
41.5
61.2
66.0
60.8
61.9
69.0
75.4
74.8
70.8
48.4
7.9
11.6
20.4
75.0
73.8
32.0
40.4
41.5
48.3
77.4
70.8
76.1
34.1
73.8
76.8
65.3
36.6
72.3
74.7
51.9
75.1
43.0
49.0
89.2
5G
EP
(0.7
,-1.
3,0)
40.2
61.8
67.0
61.8
62.2
71.9
78.7
78.3
78.3
62.9
14.6
6.6
6.7
78.2
77.7
16.8
60.5
51.5
50.5
81.1
71.9
77.3
35.5
79.2
78.1
66.4
36.3
73.4
80.0
61.7
80.0
61.8
69.6
80.9
5G
EP
(0.8
,-1,
0)49
.169
.469
.264
.869
.974
.881
.681
.584
.975
.832
.214
.18.
281
.281
.711
.577
.666
.553
.284
.875
.980
.739
.984
.781
.470
.636
.377
.184
.871
.384
.078
.284
.780
.3
5G
EP
(1,-
0.6,
0)65
.281
.573
.270
.282
.078
.285
.285
.290
.987
.159
.637
.124
.684
.786
.412
.190
.382
.356
.788
.882
.586
.248
.590
.386
.777
.936
.483
.389
.481
.587
.590
.794
.286
.6
5G
EP
(1.1
,0,0
)77
.489
.576
.875
.289
.881
.087
.787
.994
.393
.177
.759
.044
.587
.389
.915
.595
.790
.460
.091
.787
.890
.557
.093
.890
.984
.036
.288
.492
.588
.190
.195
.997
.792
.1
5G
EP
(2,2
.7,0
)91
.597
.084
.784
.797
.286
.392
.292
.497
.998
.293
.983
.771
.191
.995
.024
.799
.197
.467
.195
.894
.896
.173
.997
.896
.392
.736
.095
.196
.495
.593
.799
.299
.697
.7
5G
EP
(3,4
.6,0
)95
.898
.989
.490
.098
.989
.794
.795
.099
.199
.397
.590
.880
.394
.497
.331
.299
.799
.071
.997
.797
.598
.283
.199
.098
.396
.335
.597
.698
.197
.995
.999
.899
.999
.0
5G
EP
(0,5
00,6
00)
94.5
98.5
92.7
92.8
98.5
93.8
96.8
96.9
99.2
99.1
94.4
82.4
68.0
96.6
97.9
24.9
99.6
98.7
79.9
98.3
97.7
98.3
84.5
99.1
98.4
96.6
49.7
97.8
98.6
97.9
88.2
99.6
99.8
98.9
6G
EP
(0.4
,-2.
9,0)
62.7
80.7
78.5
75.3
81.5
79.8
84.9
84.6
79.9
59.0
8.8
19.4
38.0
84.5
83.4
54.0
48.8
59.5
59.8
86.5
83.8
87.5
51.1
84.5
87.9
79.7
45.0
84.9
84.6
64.8
78.8
52.5
56.5
97.5
6G
EP
(0.5
,-1.
9,0)
59.7
79.5
80.6
77.5
80.2
83.3
88.0
87.8
85.9
71.8
11.8
8.4
15.3
87.7
87.1
39.4
65.0
64.5
63.1
89.6
85.2
88.5
53.6
88.5
89.0
81.3
46.2
86.1
88.7
73.9
82.3
67.4
72.8
95.5
6G
EP
(0.6
,-1.
3,0)
64.1
82.6
82.8
80.2
82.9
86.2
90.8
90.7
91.4
84.1
28.5
9.1
6.3
90.5
90.6
23.7
82.6
75.8
66.7
92.6
87.5
90.5
58.0
92.4
90.9
84.0
46.7
88.3
92.4
82.8
85.1
83.5
87.9
92.5
6G
EP
(0.8
,-0.
8,0)
81.4
92.7
87.5
86.2
93.0
90.3
94.2
94.3
96.9
95.5
71.5
42.9
26.0
94.0
95.1
16.7
96.7
92.8
73.1
96.1
93.2
95.0
70.1
96.9
95.3
90.9
47.9
93.7
96.4
92.9
87.6
96.9
98.2
95.1
6G
EP
(1,0
,0)
94.4
98.4
92.6
92.6
98.5
93.7
96.7
96.8
99.1
99.1
94.1
81.9
67.6
96.6
97.9
24.7
99.6
98.7
79.4
98.3
97.7
98.3
83.8
99.1
98.4
96.6
49.1
97.8
98.5
97.9
88.0
99.6
99.8
98.9
6G
EP
(2,3
.9,0
)98
.199
.696
.196
.399
.696
.298
.398
.499
.799
.898
.391
.981
.298
.299
.233
.499
.999
.785
.199
.399
.299
.491
.899
.799
.598
.751
.699
.399
.499
.388
.899
.910
099
.7
6G
EP
(3,6
.2,0
)98
.799
.897
.397
.699
.897
.398
.998
.999
.899
.998
.893
.983
.898
.899
.436
.899
.999
.887
.899
.699
.599
.694
.399
.899
.799
.253
.199
.599
.699
.689
.110
010
099
.8
6G
EP
(0,1
40,1
29.1
)94
.898
.693
.393
.398
.694
.397
.097
.299
.399
.294
.582
.768
.496
.998
.125
.299
.698
.880
.898
.597
.998
.585
.399
.298
.596
.950
.598
.098
.798
.187
.699
.799
.899
.0
10G
EP
(0.4
,-1.
7,0)
95.0
98.7
97.7
97.5
98.7
98.2
99.1
99.1
99.4
99.0
72.8
27.2
10.4
99.0
99.2
42.4
98.8
98.0
91.2
99.4
98.9
99.2
92.0
99.6
99.3
98.4
67.0
99.0
99.5
98.7
74.0
98.9
99.4
99.5
10G
EP
(0.5
,-1,
0)98
.599
.798
.998
.999
.799
.199
.699
.799
.999
.994
.267
.739
.499
.699
.836
.999
.999
.794
.799
.899
.799
.896
.499
.999
.899
.569
.999
.799
.999
.769
.499
.999
.999
.8
10G
EP
(0.7
,0,0
)10
010
099
.999
.910
099
.899
.910
010
010
010
099
.497
.299
.910
055
.710
010
098
.410
010
010
099
.810
010
010
074
.610
010
010
051
.310
010
010
0
10G
EP
(1.4
,5.7
,0)
99.8
100
99.5
99.6
100
99.6
99.8
99.8
100
100
99.5
95.7
86.5
99.8
99.9
41.6
100
100
96.8
100
99.9
100
98.8
100
100
99.9
71.9
100
100
100
61.3
100
100
100
10G
EP
(0,6
,12.
2)99
.399
.999
.199
.199
.999
.199
.699
.699
.999
.999
.093
.181
.999
.699
.836
.410
099
.995
.099
.899
.899
.997
.699
.999
.999
.768
.499
.899
.999
.867
.210
010
099
.9
10G
EP
(0,1
7,-1
2.6)
99.5
99.9
99.1
99.2
99.9
99.2
99.7
99.7
100
100
99.0
93.4
82.2
99.7
99.9
37.1
100
99.9
95.1
99.9
99.8
99.9
97.8
100
99.9
99.7
69.0
99.8
99.9
99.9
66.5
100
100
99.9
20G
EP
(0.3
,-1.
3,0)
100
100
100
100
100
100
100
100
100
100
99.8
94.7
75.8
100
100
60.3
100
100
99.6
100
100
100
99.9
100
100
100
83.6
100
100
100
31.3
100
100
100
20G
EP
(0.5
,0,0
)10
010
010
010
010
010
010
010
010
010
010
010
010
010
010
084
.210
010
010
010
010
010
010
010
010
010
089
.210
010
010
06.
810
010
010
0
20G
EP
(0.8
,2.3
,0)
100
100
100
100
100
100
100
100
100
100
100
99.8
98.4
100
100
67.7
100
100
99.9
100
100
100
100
100
100
100
86.9
100
100
100
17.0
100
100
100
20G
EP
(0,1
4,-1
7.6)
100
100
99.9
100
100
99.9
100
100
100
100
99.9
98.2
91.9
100
100
50.2
100
100
99.2
100
100
100
99.8
100
100
100
81.2
100
100
100
36.7
100
100
100
20G
EP
(0,6
,2.6
)99
.910
099
.899
.910
099
.899
.910
010
010
099
.897
.189
.399
.910
045
.710
010
098
.510
010
010
099
.510
010
010
077
.710
010
010
045
.310
010
010
0
50G
EP
(0.3
,-0.
7,0)
100
100
100
100
100
100
100
100
100
100
100
100
99.9
100
100
89.0
100
100
100
100
100
100
100
100
100
100
93.4
100
100
100
1.4
100
100
100
50G
EP
(0.4
,0,0
)10
010
010
010
010
010
010
010
010
010
010
010
010
010
010
096
.710
010
010
010
010
010
010
010
010
010
095
.210
010
010
00.
110
010
010
0
50G
EP
(0.6
,1.2
,0)
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
93.1
100
100
100
100
100
100
100
100
100
100
95.1
100
100
100
0.3
100
100
100
50G
EP
(0,5
.1,2
.1)
100
100
99.9
100
100
99.9
100
100
100
100
99.9
98.4
92.3
100
100
51.1
100
100
99.3
100
100
100
99.8
100
100
100
81.7
100
100
100
33.3
100
100
100
50G
EP
(0,8
,-7.
2)10
010
010
010
010
010
010
010
010
010
010
099
.495
.910
010
059
.510
010
099
.810
010
010
010
010
010
010
086
.210
010
010
020
.010
010
010
0
50G
EP
(0,1
0,-1
3.8)
100
100
100
100
100
100
100
100
100
100
100
99.8
98.2
100
100
68.5
100
100
99.9
100
100
100
100
100
100
100
89.3
100
100
100
10.9
100
100
100
50G
EP
(0,1
0.8,
-17.
3)10
010
010
010
010
010
010
010
010
010
010
010
099
.310
010
077
.110
010
010
010
010
010
010
010
010
010
091
.610
010
010
05.
510
010
010
0
Mea
n
200
76.0
81.1
73.3
72.5
81.3
63.4
68.0
70.1
66.7
74.2
72.2
69.7
66.8
67.4
71.9
48.9
78.4
77.0
52.6
74.9
79.6
79.2
70.2
62.8
79.0
78.7
44.5
79.6
72.8
72.5
29.8
77.8
51.2
85.6
Ran
k
200
123
1517
.52
2824
2227
1419
2326
2520
329
1130
134.
56
2129
78
334.
516
17.5
3410
311
Dev
.to
the
Bes
t-
Mea
n
200
13.2
8.1
15.9
16.7
7.9
25.8
21.2
19.1
22.5
15.0
17.0
19.4
22.4
21.7
17.3
40.3
10.7
12.2
36.5
14.2
9.6
10.0
18.9
26.4
10.2
10.5
44.7
9.5
16.4
16.7
59.4
11.4
37.9
3.6
Ran
k
200
123
1517
.52
2824
2227
1419
2326
2520
329
1130
135
621
297
833
416
17.5
3410
311
Dev
.to
the
Bes
t-
Max
200
82.0
54.4
67.1
67.4
54.2
100
85.8
82.1
91.1
84.9
88.7
91.3
92.2
86.9
76.6
87.9
79.9
73.2
91.9
75.8
47.1
57.0
76.1
99.9
59.1
51.7
88.7
45.6
87.1
82.1
100
78.9
100
42.3
Ran
k
200
176
910
533
2118
.527
2025
.528
3022
1424
1611
2912
37
1331
84
25.5
223
18.5
3315
331
37
Tab
le7:
Pow
erag
ainst
sym
met
ric
dis
trib
uti
onfo
r5%
leve
lte
sts.M
=1,
000,
000.n
=20
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3N
(0,1
)5.
05.
05.
15.
05.
05.
04.
95.
15.
05.
05.
05.
05.
04.
95.
04.
95.
15.
05.
05.
05.
05.
05.
05.
15.
05.
05.
05.
05.
15.
05.
15.
05.
15.
1
1.5
Bet
a(0.
5,0.
5)31
.861
.577
.766
.561
.248
.00.
647
.80.
470
.327
.611
.56.
50.
627
.545
.154
.834
.72.
953
.472
.447
.788
.13.
243
.575
.249
.767
.077
.846
.51.
446
.089
.150
.4
1.51
LoC
onN
(0.5
,5)
65.3
81.3
72.0
55.0
81.1
55.2
1.1
59.5
1.3
68.0
61.3
47.4
34.6
1.1
39.4
47.7
79.4
57.6
4.6
66.8
75.3
54.6
86.3
2.1
50.7
78.2
23.6
71.3
58.6
69.0
3.2
52.8
65.3
68.0
1.63
JS
B(0
,0.5
)19
.036
.648
.835
.036
.329
.60.
425
.90.
343
.514
.67.
04.
90.
412
.225
.340
.217
.41.
939
.944
.022
.066
.06.
519
.247
.529
.938
.255
.427
.60.
834
.767
.834
.3
1.72
LoC
onN
(0.5
,4)
35.0
46.0
37.9
25.0
45.7
27.8
0.7
26.0
0.8
36.6
29.7
21.2
15.4
0.7
13.4
27.8
56.1
26.3
2.8
42.5
40.3
22.3
56.2
3.6
19.8
43.5
14.9
35.9
35.7
34.5
1.7
41.1
39.9
41.1
1.75
Tu
key(1
.5)
11.5
20.9
28.2
17.8
20.7
16.5
0.3
12.8
0.2
24.4
7.7
4.7
4.2
0.3
5.2
15.8
27.4
9.8
1.3
26.5
25.0
10.3
44.7
8.6
8.7
27.7
18.7
20.7
36.4
15.4
0.5
24.5
47.1
22.0
1.8
Tu
key(2
)9.
816
.922
.313
.516
.713
.10.
39.
70.
219
.26.
54.
44.
20.
33.
913
.423
.68.
21.
122
.519
.87.
737
.59.
06.
522
.215
.216
.230
.012
.50.
421
.439
.618
.6
1.87
JS
B(0
,0.7
)8.
613
.215
.89.
113
.19.
70.
37.
10.
314
.15.
74.
34.
20.
32.
811
.320
.36.
91.
018
.514
.55.
528
.99.
34.
616
.410
.911
.722
.410
.00.
418
.529
.415
.4
2.04
LoC
onN
(0.5
,3)
12.5
15.0
12.3
7.9
14.8
8.2
0.7
6.7
0.6
12.0
9.1
6.9
5.8
0.7
3.2
12.5
23.4
8.0
1.7
16.3
13.0
5.9
22.7
6.3
5.2
14.5
7.8
10.9
14.4
11.0
1.0
19.9
17.1
14.9
2.06
Tu
key(3
)4.
86.
16.
93.
96.
03.
70.
32.
60.
35.
63.
74.
24.
60.
31.
27.
19.
74.
70.
88.
36.
42.
314
.67.
92.
07.
36.
15.
010
.74.
60.
59.
415
.88.
0
2.1
Tu
key(0
.5)
5.5
6.6
6.4
3.8
6.5
3.8
0.4
2.8
0.4
5.7
4.0
4.0
4.3
0.4
1.4
7.3
11.0
4.8
0.9
8.7
6.3
2.5
13.6
7.8
2.1
7.1
5.5
5.1
9.5
5.2
0.6
10.4
13.0
8.1
2.14
Bet
a(2,
2)5.
15.
75.
33.
35.
63.
00.
42.
30.
54.
73.
84.
04.
30.
51.
36.
89.
44.
61.
07.
15.
32.
211
.37.
21.
96.
04.
74.
37.
74.
60.
79.
010
.77.
1
2.5
LoC
onN
(0.5
,2)
5.1
5.0
4.4
3.7
4.9
3.0
1.8
2.7
1.6
4.0
4.1
4.2
4.3
1.8
2.2
6.3
6.9
4.5
2.3
5.0
4.6
2.8
7.6
5.2
2.7
4.9
4.4
4.0
4.8
4.4
1.8
6.7
6.1
5.3
2.9
Tu
key(5
)11
.811
.34.
65.
011
.43.
33.
76.
27.
49.
320
.820
.116
.43.
75.
95.
79.
87.
34.
14.
56.
97.
95.
36.
38.
06.
43.
47.
28.
57.
39.
89.
511
.113
.8
3T
uke
y(0
.1)
4.9
4.9
4.8
4.8
4.9
4.8
4.7
4.8
4.8
4.9
5.1
5.0
5.0
4.7
4.8
4.9
4.9
4.9
4.8
4.7
4.8
4.8
4.9
4.9
4.8
4.8
4.8
4.8
4.9
4.9
4.9
4.9
4.9
4.9
3.4
JS
U(0
,1,0
,0.3
)5.
96.
57.
37.
46.
68.
28.
48.
28.
67.
45.
85.
45.
28.
48.
34.
86.
45.
97.
97.
67.
17.
95.
56.
98.
06.
96.
77.
37.
26.
88.
26.
46.
56.
6
3.91
GE
P(1
,-1.
1,0)
7.3
9.0
10.6
10.8
9.1
12.1
12.5
12.3
12.7
10.4
6.3
5.3
5.1
12.6
12.3
5.2
8.4
7.1
11.6
11.1
10.1
11.7
7.0
9.5
11.9
9.8
9.0
10.6
10.1
9.4
11.8
8.5
8.4
8.9
4S
tud
ent-
t(10
)7.
38.
810
.210
.48.
911
.812
.212
.012
.610
.46.
55.
75.
412
.212
.04.
98.
67.
411
.310
.99.
811
.46.
89.
511
.69.
58.
710
.310
.19.
311
.58.
68.
89.
1
4.2
Log
isti
c(0,
1)8.
510
.512
.012
.310
.714
.114
.714
.515
.512
.87.
66.
25.
714
.714
.64.
810
.38.
613
.413
.011
.613
.77.
411
.414
.011
.29.
912
.312
.311
.114
.110
.410
.610
.6
4.51
JS
U(0
,1,0
,0.5
)9.
011
.212
.913
.111
.415
.015
.615
.416
.313
.47.
66.
35.
715
.615
.54.
810
.99.
114
.313
.912
.414
.68.
012
.214
.912
.010
.413
.112
.911
.814
.511
.111
.211
.4
5.4
Tu
key(1
0)89
.991
.064
.073
.391
.248
.453
.163
.982
.786
.993
.991
.083
.252
.967
.350
.074
.372
.246
.159
.680
.785
.161
.882
.185
.678
.538
.182
.274
.671
.315
.389
.975
.283
.3
6L
apla
ce(0
,1)
22.1
27.2
24.7
26.2
27.6
28.5
30.1
31.6
35.4
32.6
20.4
14.0
10.6
30.0
32.1
5.5
27.4
20.3
26.8
28.3
26.1
31.3
15.4
27.7
31.9
25.0
18.0
27.8
30.0
26.3
28.1
28.7
28.2
25.8
10.4
Tu
key(2
0)99
.910
098
.399
.310
089
.892
.395
.499
.699
.899
.999
.999
.592
.197
.291
.293
.198
.785
.293
.899
.799
.898
.599
.899
.999
.773
.799
.896
.798
.30.
499
.993
.899
.2
36.1
9JS
U(0
,1,0
,1)
34.7
42.3
41.2
42.9
42.7
45.0
46.7
48.0
51.2
47.8
22.4
12.4
8.6
46.7
48.7
6.2
41.7
34.1
42.5
44.9
42.4
47.6
29.8
44.2
48.2
41.3
27.9
44.1
44.6
42.3
31.2
43.4
42.4
40.4
75.9
8JS
U(0
,1,0
,1.1
)42
.050
.047
.649
.650
.551
.153
.054
.758
.255
.527
.614
.89.
852
.955
.56.
949
.140
.948
.451
.549
.454
.736
.051
.555
.348
.231
.951
.151
.749
.531
.851
.349
.847
.5
Inf
Stu
den
t-t(
4)17
.422
.424
.425
.022
.727
.628
.728
.830
.526
.411
.27.
66.
328
.729
.15.
122
.117
.826
.226
.524
.127
.716
.124
.428
.223
.417
.625
.325
.023
.323
.022
.622
.622
.2
Inf
Stu
den
t-t(
2)45
.352
.751
.653
.253
.154
.956
.557
.760
.657
.726
.513
.58.
956
.458
.57.
151
.844
.752
.354
.952
.857
.540
.854
.558
.051
.834
.554
.454
.352
.829
.153
.752
.450
.7
Inf
Stu
den
t-t(
1)84
.488
.184
.486
.288
.384
.786
.187
.790
.290
.065
.337
.420
.786
.088
.517
.986
.081
.782
.185
.986
.689
.078
.688
.189
.386
.059
.687
.486
.786
.813
.988
.786
.385
.5
Mea
n
2025
.330
.630
.127
.530
.625
.918
.926
.921
.431
.421
.816
.914
.218
.923
.916
.331
.123
.318
.029
.730
.627
.032
.322
.026
.531
.119
.729
.832
.127
.29.
529
.934
.229
.2
Ran
k
2021
810
158
2028
.518
264
2531
3328
.522
325.
523
3013
817
224
195.
527
123
1634
111
14
Dev
.to
the
Bes
t-
Mea
n
2014
.18.
99.
412
.08.
813
.520
.512
.618
.18.
117
.622
.525
.220
.515
.523
.18.
316
.121
.49.
78.
812
.47.
117
.512
.98.
419
.89.
77.
412
.229
.99.
55.
210
.2
Ran
k
2021
910
157.
520
28.5
1826
425
3133
28.5
2232
523
3012
.57.
517
224
196
2712
.53
1634
111
14
Dev
.to
the
Bes
t-
Max
2057
.331
.229
.932
.831
.545
.588
.541
.988
.724
.361
.577
.682
.688
.561
.672
.334
.354
.486
.235
.723
.845
.832
.185
.948
.620
.362
.729
.627
.742
.699
.643
.121
.038
.7
Ran
k
2022
87
119
1831
.515
334
2327
2831
.524
2612
2130
133
1910
2920
125
65
1634
172
14
38
Tab
le8:
Pow
erag
ainst
sym
met
ric
dis
trib
uti
onfo
r5%
leve
lte
sts.M
=1,
000,
000.n
=50
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3N
(0,1
)5.
05.
05.
05.
05.
05.
15.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
04.
95.
05.
05.
05.
05.
05.
05.
15.
05.
05.
05.
04.
95.
05.
05.
05.
0
1.5
Bet
a(0.
5,0.
5)80
.099
.110
010
099
.199
.538
.397
.50.
099
.682
.951
.229
.935
.497
.170
.096
.491
.714
.696
.599
.999
.210
011
.998
.810
094
.199
.910
097
.60.
093
.210
095
.3
1.51
LoC
onN
(0.5
,5)
99.2
100
99.6
98.9
100
99.4
43.3
98.1
0.2
99.9
99.9
99.5
98.5
40.2
98.9
68.0
99.5
99.7
16.7
97.5
99.9
99.3
99.9
0.8
99.0
99.9
46.5
99.8
98.4
99.9
0.2
90.1
89.2
98.5
1.63
JS
B(0
,0.5
)54
.990
.198
.798
.390
.396
.39.
484
.10.
095
.158
.830
.217
.28.
283
.041
.488
.072
.16.
790
.397
.286
.899
.838
.983
.698
.280
.595
.799
.386
.80.
084
.699
.583
.5
1.72
LoC
onN
(0.5
,4)
82.8
94.2
86.0
79.9
94.3
89.8
5.6
73.3
0.1
93.8
90.8
83.3
74.5
4.9
76.8
42.9
96.5
89.7
6.9
86.5
90.1
77.8
95.3
11.5
74.6
92.4
29.9
88.2
88.0
90.7
0.1
86.9
62.3
90.2
1.75
Tu
key(1
.5)
31.9
67.8
89.9
87.9
68.0
84.9
1.5
56.7
0.0
79.3
32.6
14.8
9.0
1.3
55.0
23.2
71.5
46.8
3.0
74.7
84.0
58.5
97.0
54.5
53.1
88.3
64.1
79.0
94.8
63.7
0.0
68.8
95.1
62.1
1.8
Tu
key(2
)26
.057
.782
.679
.458
.078
.00.
845
.90.
070
.526
.012
.07.
60.
644
.218
.964
.638
.92.
366
.875
.046
.293
.856
.241
.080
.755
.668
.890
.754
.20.
062
.390
.353
.6
1.87
JS
B(0
,0.7
)21
.345
.266
.160
.645
.566
.80.
333
.00.
058
.221
.510
.77.
10.
331
.815
.556
.831
.61.
756
.058
.430
.584
.554
.826
.165
.538
.351
.780
.743
.30.
054
.874
.843
.7
2.04
LoC
onN
(0.5
,3)
31.8
44.4
34.4
29.7
44.7
43.7
0.3
20.2
0.1
47.2
38.1
28.1
21.5
0.3
20.3
17.9
62.2
37.1
2.0
39.4
37.7
20.6
55.0
26.8
17.9
43.1
14.4
33.7
47.0
38.0
0.1
57.0
24.5
41.9
2.06
Tu
key(3
)7.
716
.633
.829
.316
.631
.30.
08.
90.
022
.65.
94.
44.
40.
07.
97.
525
.011
.30.
622
.926
.48.
657
.838
.96.
832
.623
.020
.949
.314
.90.
024
.847
.717
.2
2.1
Tu
key(0
.5)
9.8
17.3
24.3
20.2
17.4
29.2
0.0
8.8
0.0
23.1
8.7
5.7
4.9
0.1
7.9
8.7
29.3
13.5
0.8
22.6
20.9
7.3
45.8
36.5
5.9
26.1
14.4
16.8
41.0
16.4
0.0
28.6
29.9
17.8
2.14
Bet
a(2,
2)8.
313
.317
.514
.413
.421
.70.
16.
10.
017
.37.
25.
24.
70.
15.
37.
823
.710
.90.
716
.615
.35.
036
.230
.34.
019
.411
.112
.131
.512
.50.
023
.321
.513
.8
2.5
LoC
onN
(0.5
,2)
6.8
7.8
6.1
6.3
7.8
7.2
0.8
3.0
0.6
7.9
6.3
5.4
5.0
0.8
2.3
7.0
12.7
7.1
1.8
5.6
6.5
2.9
13.4
10.7
2.5
8.0
5.7
5.5
9.6
6.7
0.5
12.4
5.0
6.8
2.9
Tu
key(5
)23
.624
.84.
13.
525
.10.
81.
11.
76.
213
.142
.445
.641
.31.
14.
17.
719
.813
.31.
92.
913
.010
.613
.87.
110
.511
.71.
111
.75.
39.
39.
620
.228
.033
.3
3T
uke
y(0
.1)
5.0
4.9
4.3
4.5
4.9
4.3
4.2
4.3
4.4
4.8
5.1
5.0
5.0
4.3
4.4
4.9
4.8
4.8
4.5
4.3
4.6
4.5
4.9
4.6
4.5
4.6
4.5
4.5
4.7
4.8
4.5
4.8
4.8
4.5
3.4
JS
U(0
,1,0
,0.3
)6.
37.
59.
68.
87.
510
.612
.011
.412
.28.
76.
15.
65.
412
.011
.74.
98.
06.
710
.011
.79.
210
.95.
29.
011
.28.
58.
09.
79.
77.
612
.28.
110
.09.
6
3.91
GE
P(1
,-1.
1,0)
8.7
12.2
16.5
15.0
12.3
18.4
21.1
20.5
21.1
14.2
6.9
5.6
5.2
21.1
20.8
5.6
12.4
9.6
16.5
20.9
15.9
19.4
7.2
16.1
19.9
14.5
12.2
16.9
17.4
12.5
21.7
12.7
15.6
16.8
4S
tud
ent-
t(10
)8.
912
.116
.314
.712
.218
.220
.619
.921
.314
.67.
66.
25.
720
.620
.44.
813
.710
.616
.320
.515
.618
.97.
516
.119
.314
.312
.016
.617
.212
.520
.813
.917
.316
.5
4.2
Log
isti
c(0,
1)11
.316
.119
.918
.116
.222
.525
.725
.327
.619
.79.
97.
36.
425
.825
.94.
818
.913
.919
.726
.019
.724
.18.
621
.324
.617
.914
.021
.023
.016
.527
.219
.123
.721
.0
4.51
JS
U(0
,1,0
,0.5
)12
.117
.422
.120
.117
.524
.728
.027
.529
.621
.19.
77.
26.
328
.028
.14.
820
.315
.121
.728
.321
.726
.210
.023
.226
.819
.915
.423
.024
.817
.928
.520
.525
.123
.0
5.4
Tu
key(1
0)99
.910
094
.997
.310
066
.378
.884
.599
.399
.810
010
010
078
.794
.683
.598
.699
.764
.692
.899
.799
.797
.999
.599
.799
.533
.699
.796
.998
.210
.610
099
.099
.7
6L
apla
ce(0
,1)
43.4
54.6
45.5
45.3
55.2
48.9
55.4
56.7
65.6
61.6
42.5
29.5
22.1
55.4
59.8
7.1
62.7
50.7
41.5
59.3
52.1
59.1
26.8
59.7
60.0
48.3
26.9
54.2
60.8
51.4
54.7
64.0
69.3
57.5
10.4
Tu
key(2
0)10
010
010
010
010
099
.699
.999
.910
010
010
010
010
099
.910
099
.910
010
099
.010
010
010
010
010
010
010
087
.210
010
010
00.
010
010
010
0
36.1
9JS
U(0
,1,0
,1)
64.6
76.0
72.6
72.7
76.3
74.9
79.4
80.2
84.2
80.5
46.8
25.0
15.7
79.4
81.9
8.2
80.3
72.9
67.2
81.6
76.4
80.9
55.7
81.2
81.4
73.9
45.3
77.8
81.4
75.6
46.5
81.1
84.1
78.4
75.9
8JS
U(0
,1,0
,1.1
)75
.184
.380
.380
.784
.681
.885
.686
.489
.987
.857
.932
.019
.785
.688
.09.
987
.681
.974
.687
.684
.087
.466
.287
.987
.882
.050
.985
.087
.883
.740
.388
.390
.285
.6
Inf
Stu
den
t-t(
4)30
.742
.046
.144
.242
.449
.553
.954
.057
.047
.518
.310
.58.
053
.954
.95.
347
.238
.643
.455
.146
.952
.727
.551
.053
.444
.329
.248
.752
.142
.944
.647
.752
.948
.8
Inf
Stu
den
t-t(
2)77
.985
.984
.084
.186
.285
.388
.288
.891
.188
.855
.328
.016
.688
.289
.89.
488
.683
.979
.589
.686
.489
.272
.189
.489
.584
.855
.387
.389
.385
.833
.489
.190
.887
.5
Inf
Stu
den
t-t(
1)99
.499
.799
.399
.599
.799
.299
.599
.699
.899
.897
.081
.256
.799
.599
.734
.399
.899
.698
.499
.799
.699
.898
.699
.899
.899
.678
.899
.799
.799
.72.
899
.899
.999
.7
Mea
n
5040
.449
.952
.150
.750
.052
.130
.746
.529
.152
.938
.930
.125
.130
.447
.122
.553
.444
.925
.852
.252
.247
.553
.140
.846
.753
.034
.251
.257
.348
.113
.052
.255
.650
.4
Ran
k
5024
1610
.513
1510
.527
2130
625
2932
2819
333
2231
88
184
2320
526
121
1734
82
14
Dev
.to
the
Bes
t-
Mea
n
5021
.912
.510
.311
.712
.410
.331
.715
.933
.39.
523
.532
.237
.332
.015
.339
.99.
017
.536
.610
.210
.214
.89.
321
.615
.79.
428
.211
.25.
114
.249
.410
.26.
812
.0
Ran
k
5024
1610
.513
1510
.527
2130
625
2932
2819
333
2231
88
184
2320
526
121
1734
82
14
Dev
.to
the
Bes
t-
Max
5067
.841
.241
.542
.141
.244
.895
.551
.510
035
.267
.882
.288
.095
.752
.781
.732
.854
.994
.042
.732
.654
.042
.599
.258
.433
.966
.636
.940
.342
.910
033
.037
.740
.8
Ran
k
5024
.510
.512
1310
.517
3018
33.5
524
.527
2831
1926
221
2915
120
1432
224
236
816
33.5
37
9
39
Tab
le9:
Pow
erag
ainst
sym
met
ric
dis
trib
uti
onfo
r5%
leve
lte
sts.M
=1,
000,
000.n
=10
0
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3N
(0,1
)5.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
04.
95.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
15.
05.
05.
05.
05.
05.
05.
05.
0
1.5
Bet
a(0.
5,0.
5)99
.410
010
010
010
096
.810
010
062
.010
099
.388
.466
.310
010
093
.410
099
.970
.910
010
010
010
036
.810
010
010
010
010
010
00.
099
.910
010
0
1.51
LoC
onN
(0.5
,5)
100
100
100
100
100
97.3
100
100
83.9
100
100
100
100
100
100
82.3
100
100
74.3
100
100
100
100
1.5
100
100
71.2
100
100
100
0.0
99.3
93.0
100
1.63
JS
B(0
,0.5
)92
.010
010
010
010
010
098
.899
.916
.810
092
.866
.142
.398
.899
.970
.099
.798
.144
.599
.910
010
010
084
.610
010
099
.610
010
099
.90.
099
.510
099
.7
1.72
LoC
onN
(0.5
,4)
99.5
100
99.6
99.3
100
99.9
91.8
98.8
18.1
100
99.9
99.7
99.0
91.5
99.4
61.2
100
99.9
38.1
99.7
99.9
99.6
100
42.1
99.4
99.9
49.7
99.9
99.7
99.9
0.0
99.2
64.1
99.9
1.75
Tu
key(1
.5)
68.7
98.0
100
100
98.1
99.9
85.4
98.0
1.9
99.1
69.3
36.0
20.3
84.9
97.1
40.7
96.8
86.7
21.6
99.0
99.9
98.9
100
95.0
98.3
100
97.9
99.8
100
97.3
0.0
96.3
100
95.9
1.8
Tu
key(2
)58
.694
.999
.999
.995
.199
.774
.295
.10.
797
.659
.128
.616
.373
.593
.432
.394
.279
.615
.797
.899
.696
.510
095
.695
.099
.895
.999
.310
094
.20.
093
.699
.791
.9
1.87
JS
B(0
,0.7
)48
.387
.099
.099
.087
.498
.655
.087
.40.
293
.650
.524
.714
.654
.284
.525
.690
.070
.410
.294
.797
.186
.499
.995
.082
.898
.584
.795
.799
.787
.60.
089
.295
.584
.5
2.04
LoC
onN
(0.5
,3)
63.8
81.8
69.6
66.5
82.3
82.4
22.4
56.5
0.1
86.6
77.4
64.1
52.5
21.9
58.6
28.3
92.7
77.6
6.8
77.2
75.0
58.5
85.2
70.2
54.5
80.1
24.5
72.4
82.8
78.5
0.0
90.4
18.9
80.1
2.06
Tu
key(3
)14
.744
.288
.489
.444
.779
.610
.542
.10.
055
.711
.45.
54.
710
.136
.08.
851
.626
.52.
261
.876
.645
.097
.081
.038
.884
.469
.770
.092
.643
.20.
051
.678
.042
.2
2.1
Tu
key(0
.5)
19.2
42.6
71.1
70.4
43.2
75.8
8.8
38.3
0.0
56.9
19.4
10.0
7.1
8.5
34.1
11.4
59.0
32.6
2.4
60.1
60.2
32.1
88.4
79.8
27.3
69.6
41.2
53.9
86.0
45.2
0.0
58.6
42.2
42.9
2.14
Bet
a(2,
2)15
.031
.855
.854
.932
.463
.14.
526
.30.
044
.414
.78.
16.
24.
322
.89.
649
.025
.01.
746
.745
.420
.978
.270
.717
.255
.330
.539
.375
.234
.00.
048
.726
.532
.2
2.5
LoC
onN
(0.5
,2)
10.0
13.4
10.9
12.3
13.7
15.7
0.8
5.8
0.2
16.3
11.3
8.3
6.9
0.8
4.3
8.3
23.7
12.0
1.8
10.7
11.2
5.1
22.2
22.3
4.2
14.6
7.8
9.7
19.3
12.2
0.1
23.5
1.7
11.7
2.9
Tu
key(5
)44
.752
.016
.511
.252
.70.
30.
40.
56.
722
.271
.376
.472
.70.
43.
816
.138
.727
.51.
42.
637
.825
.053
.49.
823
.539
.32.
633
.03.
115
.08.
439
.152
.768
.1
3T
uke
y(0
.1)
4.9
4.9
3.9
4.3
4.9
3.9
3.8
3.9
4.0
4.7
5.1
5.0
5.1
3.8
3.7
5.0
4.7
4.9
4.3
3.8
4.3
4.1
4.8
4.4
4.0
4.4
4.1
4.2
4.4
4.8
4.2
4.7
4.8
4.2
3.4
JS
U(0
,1,0
,0.3
)6.
88.
512
.49.
98.
513
.416
.215
.316
.610
.26.
65.
85.
516
.215
.94.
910
.27.
911
.516
.311
.714
.54.
812
.214
.810
.49.
412
.513
.38.
717
.510
.214
.813
.1
3.91
GE
P(1
,-1.
1,0)
10.3
16.5
23.8
19.4
16.6
26.3
31.5
30.4
31.3
19.3
7.5
5.6
5.3
31.5
31.0
6.6
18.1
13.2
20.5
32.5
23.4
28.9
7.8
26.3
29.6
20.6
15.4
25.1
28.1
17.2
34.6
18.3
25.0
27.1
4S
tud
ent-
t(10
)10
.716
.223
.719
.416
.325
.930
.729
.631
.819
.88.
96.
86.
130
.730
.25.
021
.015
.120
.631
.522
.927
.98.
425
.828
.520
.415
.724
.427
.216
.932
.721
.028
.725
.7
4.2
Log
isti
c(0,
1)15
.323
.929
.724
.924
.233
.239
.438
.542
.229
.513
.08.
77.
239
.439
.25.
331
.422
.425
.341
.130
.536
.810
.736
.237
.527
.018
.532
.437
.924
.944
.031
.440
.934
.1
4.51
JS
U(0
,1,0
,0.5
)16
.726
.233
.628
.626
.436
.943
.042
.145
.431
.612
.88.
57.
143
.042
.75.
333
.824
.728
.544
.734
.040
.213
.039
.441
.030
.520
.835
.941
.027
.345
.833
.843
.137
.6
5.4
Tu
key(1
0)10
010
010
010
010
089
.296
.497
.610
010
010
010
010
096
.399
.998
.310
010
091
.099
.810
010
010
010
010
010
024
.310
099
.910
04.
410
010
010
0
6L
apla
ce(0
,1)
70.4
82.7
69.7
68.9
83.1
72.1
79.9
80.6
88.9
87.5
70.7
53.0
40.5
79.9
83.7
13.1
90.2
82.6
57.3
84.7
79.7
84.1
49.1
87.3
84.6
76.0
36.6
81.0
86.2
80.0
74.7
90.6
94.0
85.4
10.4
Tu
key(2
0)10
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
095
.910
010
010
00.
010
010
010
0
36.1
9JS
U(0
,1,0
,1)
89.0
95.3
93.0
92.8
95.4
93.8
96.1
96.3
97.8
96.9
74.5
43.8
26.6
96.1
96.9
14.9
97.3
95.1
86.2
97.2
95.5
96.7
83.4
97.5
96.9
94.4
62.3
95.8
97.3
95.3
46.9
97.4
98.4
96.5
75.9
8JS
U(0
,1,0
,1.1
)95
.198
.296
.696
.798
.396
.998
.298
.399
.198
.985
.856
.535
.298
.298
.719
.699
.198
.191
.998
.898
.198
.791
.499
.198
.797
.668
.498
.398
.998
.235
.499
.199
.598
.6
Inf
Stu
den
t-t(
4)48
.965
.168
.865
.565
.571
.977
.477
.380
.370
.628
.914
.710
.277
.477
.96.
873
.464
.059
.779
.471
.276
.344
.877
.576
.967
.941
.872
.878
.066
.661
.373
.579
.874
.4
Inf
Stu
den
t-t(
2)95
.998
.497
.797
.798
.598
.098
.898
.899
.399
.082
.948
.928
.498
.899
.017
.299
.198
.394
.799
.198
.599
.093
.999
.299
.098
.273
.298
.799
.298
.525
.099
.199
.598
.9
Inf
Stu
den
t-t(
1)10
010
010
010
010
010
010
010
010
010
010
098
.487
.710
010
065
.110
010
010
010
010
010
010
010
010
010
089
.310
010
010
00.
210
010
010
0
Mea
n
100
53.7
63.8
66.7
65.6
64.0
67.0
56.0
62.9
40.4
65.9
52.8
42.0
35.0
55.9
62.8
30.7
67.1
59.5
38.9
67.3
67.1
63.6
65.8
60.5
62.8
67.6
48.4
66.4
70.5
62.5
15.7
66.9
64.5
66.1
Ran
k
100
2616
813
156
2418
3011
2729
3225
19.5
334.
523
313
4.5
1712
2219
.52
289
121
347
1410
Dev
.to
the
Bes
t-
Mea
n
100
21.8
11.7
8.7
9.9
11.4
8.5
19.4
12.5
35.0
9.6
22.7
33.4
40.5
19.6
12.7
44.7
8.4
15.9
36.6
8.2
8.4
11.9
9.7
14.9
12.7
7.8
27.0
9.1
4.9
12.9
59.7
8.6
11.0
9.4
Ran
k
100
2616
813
156
2418
3011
2729
3225
19.5
334.
523
313
4.5
1712
2219
.52
289
121
347
1410
Dev
.to
the
Bes
t-
Max
100
82.3
52.8
59.9
65.2
52.3
76.1
86.5
75.9
99.7
54.2
85.6
91.5
92.3
86.9
72.6
88.2
45.4
70.5
94.8
73.8
38.6
57.3
44.9
98.5
61.1
37.1
75.7
43.4
73.3
61.4
100
45.4
73.8
54.8
Ran
k
100
248
1215
723
2622
339
2529
3027
1728
5.5
1631
19.5
211
432
131
213
1814
345.
519
.510
40
Tab
le10
:P
ower
agai
nst
sym
met
ric
dis
trib
uti
onfo
r5%
leve
lte
sts.M
=1,
000,
000.n
=20
0
β2
Alt
ern
ativ
eK−S
AD∗
ZC
ZA
PS
K2
JB
DH
RJB
TLmom
T(1
)Lmom
T(2
)Lmom
T(3
)Lmom
BM
3−
4BM
3−
6TMC−LR
Tw
TMC−LR−Tw
TS,5
TK,5
WWSFWRG
Da
rCS
QBCMR
β2 3
TEP
I nRsJ
SRn
3N
(0,1
)5.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
05.
04.
95.
04.
95.
05.
05.
05.
15.
05.
05.
05.
05.
05.
05.
04.
95.
05.
05.
05.
0
1.5
Bet
a(0.
5,0.
5)10
010
010
010
010
049
.210
010
010
010
010
099
.795
.210
010
099
.710
010
099
.910
010
010
010
078
.710
010
010
010
010
010
00.
010
010
010
0
1.51
LoC
onN
(0.5
,5)
100
100
100
100
100
54.7
100
100
100
100
100
100
100
100
100
91.3
100
100
100
100
100
100
100
6.5
100
100
89.7
100
100
100
0.0
100
92.4
100
1.63
JS
B(0
,0.5
)10
010
010
010
010
097
.710
010
010
010
099
.995
.278
.810
010
093
.410
010
098
.010
010
010
010
099
.610
010
010
010
010
010
00.
010
010
010
0
1.72
LoC
onN
(0.5
,4)
100
100
100
100
100
99.8
100
100
100
100
100
100
100
100
100
77.5
100
100
94.6
100
100
100
100
89.3
100
100
71.8
100
100
100
0.0
100
55.1
100
1.75
Tu
key(1
.5)
97.9
100
100
100
100
100
100
100
99.6
100
96.3
71.3
45.1
100
100
67.4
100
99.8
85.1
100
100
100
100
100
100
100
100
100
100
100
0.0
100
100
100
1.8
Tu
key(2
)94
.610
010
010
010
010
010
010
098
.610
091
.960
.536
.110
010
055
.299
.999
.275
.610
010
010
010
010
010
010
010
010
010
010
00.
099
.910
010
0
1.87
JS
B(0
,0.7
)88
.099
.910
010
099
.910
099
.910
094
.399
.986
.253
.632
.199
.999
.944
.299
.797
.759
.910
010
010
010
010
010
010
099
.910
010
099
.90.
099
.799
.899
.9
2.04
LoC
onN
(0.5
,3)
94.7
99.3
96.3
95.6
99.3
98.9
89.3
94.8
79.6
99.7
98.6
95.0
88.8
89.3
95.3
44.2
99.9
98.9
35.2
98.8
98.4
96.0
99.0
97.8
95.0
98.9
39.9
98.1
99.0
99.1
0.0
99.8
8.1
99.2
2.06
Tu
key(3
)35
.688
.810
010
088
.899
.688
.495
.136
.290
.924
.58.
75.
788
.487
.411
.485
.060
.815
.797
.799
.997
.810
099
.196
.710
099
.699
.710
086
.60.
084
.796
.489
.0
2.1
Tu
key(0
.5)
43.9
84.4
99.5
99.7
84.8
99.2
84.0
92.7
38.0
91.8
42.7
20.5
12.5
84.1
85.1
16.6
90.3
70.5
15.3
97.3
97.9
89.2
99.9
99.1
85.9
99.1
89.6
96.8
99.9
87.5
0.0
90.0
51.4
86.7
2.14
Bet
a(2,
2)33
.371
.197
.297
.971
.696
.968
.082
.522
.382
.532
.315
.710
.168
.170
.513
.282
.557
.89.
592
.492
.474
.899
.697
.369
.596
.077
.889
.599
.275
.80.
082
.126
.774
.6
2.5
LoC
onN
(0.5
,2)
17.8
27.1
22.0
25.3
27.5
33.7
7.3
16.2
1.6
34.7
23.1
15.8
11.9
7.4
11.3
10.6
44.8
24.9
2.8
27.3
23.5
13.1
37.9
44.3
11.2
29.1
11.6
21.3
39.2
25.8
0.0
44.2
0.1
25.1
2.9
Tu
key(5
)77
.688
.575
.669
.988
.90.
30.
10.
29.
540
.994
.796
.895
.50.
25.
233
.769
.957
.61.
43.
388
.573
.297
.715
.869
.991
.216
.984
.52.
630
.97.
170
.580
.796
.9
3T
uke
y(0
.1)
4.9
4.9
3.5
4.2
4.8
3.7
3.4
3.6
3.7
4.7
5.1
5.1
5.0
3.4
3.1
4.9
4.6
4.9
4.2
3.3
4.1
3.7
5.0
4.2
3.6
4.2
3.7
4.0
4.2
4.8
3.9
4.6
4.8
3.8
3.4
JS
U(0
,1,0
,0.3
)7.
710
.516
.311
.610
.418
.422
.421
.223
.212
.87.
16.
05.
622
.521
.85.
014
.29.
913
.323
.515
.920
.04.
718
.120
.513
.311
.117
.119
.511
.025
.714
.321
.018
.4
3.91
GE
P(1
,-1.
1,0)
14.3
25.6
35.4
28.2
25.5
40.3
47.4
46.4
46.7
28.6
8.3
5.7
5.6
47.4
45.8
8.0
28.4
20.2
25.8
50.3
37.2
44.2
10.9
44.1
45.0
32.0
20.0
39.2
46.3
26.8
54.0
28.8
37.7
44.3
4S
tud
ent-
t(10
)14
.824
.535
.127
.824
.539
.545
.944
.847
.629
.511
.17.
66.
446
.044
.75.
434
.324
.026
.448
.435
.842
.411
.442
.443
.131
.220
.837
.744
.126
.250
.434
.444
.140
.3
4.2
Log
isti
c(0,
1)24
.339
.445
.138
.139
.651
.459
.058
.362
.946
.818
.811
.08.
259
.158
.06.
352
.538
.833
.362
.749
.256
.217
.159
.557
.043
.524
.551
.160
.641
.566
.552
.762
.854
.4
4.51
JS
U(0
,1,0
,0.5
)26
.442
.750
.943
.842
.856
.763
.863
.266
.949
.518
.210
.57.
963
.962
.76.
155
.842
.538
.267
.154
.160
.921
.263
.561
.648
.628
.456
.064
.745
.168
.055
.965
.559
.1
5.4
Tu
key(1
0)10
010
010
010
010
099
.710
010
010
010
010
010
010
010
010
010
010
010
099
.910
010
010
010
010
010
010
011
.010
010
010
00.
810
010
010
0
6L
apla
ce(0
,1)
94.4
98.4
92.5
92.5
98.4
93.7
96.6
96.8
99.1
99.1
94.1
81.8
67.6
96.6
97.8
25.1
99.6
98.6
79.6
98.3
97.5
98.2
83.8
99.1
98.3
96.5
49.3
97.7
98.5
97.8
88.3
99.6
99.8
98.9
10.4
Tu
key(2
0)10
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
010
099
.510
010
010
00.
010
010
010
0
36.1
9JS
U(0
,1,0
,1)
99.3
99.9
99.7
99.7
99.9
99.8
99.9
99.9
100
99.9
95.4
71.0
45.1
99.9
99.9
28.5
100
99.9
98.1
99.9
99.9
99.9
98.7
100
99.9
99.8
80.0
99.9
100
99.9
45.6
100
100
99.9
75.9
8JS
U(0
,1,0
,1.1
)99
.910
099
.999
.910
099
.910
010
010
010
098
.884
.659
.410
010
038
.310
010
099
.410
010
010
099
.710
010
010
085
.310
010
010
029
.210
010
010
0
Inf
Stu
den
t-t(
4)75
.389
.290
.088
.289
.392
.494
.894
.996
.191
.747
.322
.213
.594
.894
.89.
694
.089
.379
.596
.092
.594
.572
.995
.994
.790
.658
.393
.195
.890
.472
.294
.196
.294
.1
Inf
Stu
den
t-t(
2)99
.910
010
010
010
010
010
010
010
010
098
.176
.847
.910
010
032
.710
010
099
.810
010
010
099
.910
010
010
088
.810
010
010
015
.410
010
010
0
Inf
Stu
den
t-t(
1)10
010
010
010
010
010
010
010
010
010
010
010
099
.310
010
091
.510
010
010
010
010
010
010
010
010
010
095
.710
010
010
00.
010
010
010
0
Mea
n
200
66.1
75.0
77.3
76.0
75.0
72.5
74.1
75.6
69.0
75.3
64.2
54.3
46.0
74.1
74.6
40.2
77.2
71.4
57.0
77.5
78.3
77.5
73.7
73.5
77.0
77.8
59.9
78.2
77.8
73.4
19.0
77.2
69.6
78.2
Ran
k
200
2715
.58
1215
.523
18.5
1326
1428
3132
18.5
1733
9.5
2430
6.5
16.
520
2111
4.5
292.
54.
522
349.
525
2.5
Dev
.to
the
Bes
t-
Mea
n
200
16.5
7.6
5.3
6.6
7.6
10.1
8.5
7.0
13.6
7.3
18.4
28.3
36.6
8.5
8.0
42.4
5.4
11.2
25.6
5.0
4.3
5.1
8.9
9.1
5.6
4.8
22.7
4.4
4.8
9.2
63.6
5.4
13.0
4.4
Ran
k
200
2715
.58
1215
.523
18.5
1326
1428
3132
18.5
1733
9.5
2430
61
720
2111
4.5
292.
54.
522
349.
525
2.5
Dev
.to
the
Bes
t-
Max
200
66.3
28.5
22.8
28.4
28.5
97.4
97.6
97.5
88.2
56.8
75.5
91.3
94.3
97.5
92.5
88.6
27.8
41.8
96.3
94.4
21.3
31.7
49.4
93.5
33.6
23.0
89.0
23.5
95.1
66.8
100
27.2
91.8
25.0
Ran
k
200
169.
52
89.
530
3331
.519
1518
2226
31.5
2420
713
2927
111
1425
123
214
2817
346
235
41
−2 −1 0 1 2
0.0
0.5
1.0
1.5
GEP densities with a kurtosis of 1.1
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
GEP densities with a kurtosis of 1.5
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
GEP densities with a kurtosis of 1.84
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.1
0.2
0.3
0.4
0.5
0.6
GEP densities with a kurtosis of 2
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 2.25
X
Den
sitie
s
−4 −2 0 2 4
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 2.5
X
Den
sitie
s
Figure 1: GEP densities with different tails behaviour
42
−4 −2 0 2 4
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 2.75
X
Den
sitie
s
−4 −2 0 2 4
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 3
X
Den
sitie
s
−4 −2 0 2 4
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 3.5
X
Den
sitie
s
−4 −2 0 2 4
0.0
0.2
0.4
0.6
GEP densities with a kurtosis of 4
X
Den
sitie
s
−4 −2 0 2 4
0.0
0.2
0.4
0.6
GEP densities with a kurtosis of 4.5
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.2
0.4
0.6
GEP densities with a kurtosis of 5
X
Den
sitie
s
Figure 2: GEP densities with different tails behaviour
43
−3 −2 −1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
GEP densities with a kurtosis of 6
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.2
0.4
0.6
0.8
1.0
GEP densities with a kurtosis of 10
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.5
1.0
1.5
2.0
GEP densities with a kurtosis of 20
X
Den
sitie
s
−3 −2 −1 0 1 2 3
0.0
0.5
1.0
1.5
2.0
2.5
GEP densities with a kurtosis of 50
X
Den
sitie
s
Figure 3: GEP densities with different tails behaviour
44