##################################################
Distribution  GeneralizedExtremeValue(mu=2, sigma=1.5, xi=-0.15)
Elliptical =  False
Continuous =  True
oneRealization= [2.00915]
oneSample first= [0.788048]  last= [2.8505]
mean= [2.65453]
covariance= [[ 2.73151 ]]
Kolmogorov test for the generator, sample size= 100  is  True
Kolmogorov test for the generator, sample size= 10000  is  True
Point=  [1.0]
ddf     = [0.108952]
ddf (FD)= 0.10895225309
log pdf= -1.75315345339
pdf     = 0.17322681854
pdf (FD)= 0.173226818544
cdf= 0.151407657069
ccdf= 0.848592342931
survival= 0.848592342931
Inverse survival= [5.59515]
Survival(inverse survival)= 0.05
pdf gradient     = []
pdf gradient (FD)= [-0.108952,-0.0428497,0.0749046]
cdf gradient     = []
cdf gradient (FD)= [-0.173227,0.115485,-0.0559084]
quantile= [5.59515]
cdf(quantile)= 0.95
Minimum volume interval= [-0.359967, 5.97545]
threshold= 0.95
Minimum volume level set= {x | f(x) <= 3.31111} with f=
MinimumVolumeLevelSetEvaluation(GeneralizedExtremeValue(mu=2, sigma=1.5, xi=-0.15))
beta= 0.036475780379
Bilateral confidence interval= [-0.162817, -0.162817]
beta= 0.95
Unilateral confidence interval (lower tail)= [-4.83649, 5.59515]
beta= 0.95
Unilateral confidence interval (upper tail)= [5.59515, 12]
beta= 0.95
mean= [2.66959]
standard deviation= [1.64028]
skewness= [0.435743]
kurtosis= [3.13766]
covariance= [[ 2.69053 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[mu : 2, sigma : 1.5, xi : -0.15]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [2.66959]
standard moment n= 2 , value= [9.81725]
standard moment n= 3 , value= [42.4963]
standard moment n= 4 , value= [209.086]
standard moment n= 5 , value= [1135.1]
Standard representative= RandomMixture(-Weibull(alpha = 10, beta = 6.66667, gamma = -12))
mu= 2.0
sigma= 1.5
xi= -0.15
Actual distribution= RandomMixture(-Weibull(alpha = 10, beta = 6.66667, gamma = -12))
Distribution from actual distribution= GeneralizedExtremeValue(mu=-2, sigma=-1.5, xi=-0.15)
##################################################
Distribution  GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0)
Elliptical =  False
Continuous =  True
oneRealization= [2.21357]
oneSample first= [0.88405]  last= [4.65486]
mean= [2.86083]
covariance= [[ 3.68655 ]]
Kolmogorov test for the generator, sample size= 100  is  True
Kolmogorov test for the generator, sample size= 10000  is  True
Point=  [1.0]
ddf     = [0.116989]
ddf (FD)= 0.116988580193
log pdf= -1.6865324825
pdf     = 0.185160459257
pdf (FD)= 0.185160459255
cdf= 0.142596824326
ccdf= 0.857403175674
survival= 0.857403175674
Inverse survival= [0.354217]
Survival(inverse survival)= 0.95
pdf gradient     = [0.102258,-0.116989]
pdf gradient (FD)= [-0.116989,-0.0454479,0.0844441]
cdf gradient     = [-0.277741,-0.18516]
cdf gradient (FD)= [-0.18516,0.12344,-0.0617202]
quantile= [6.45529]
cdf(quantile)= 0.95
Minimum volume interval= [-0.341999, 6.74221]
threshold= 0.95
Minimum volume level set= {x | f(x) <= 3.6093} with f=
MinimumVolumeLevelSetEvaluation(GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0))
beta= 0.0270707759809
Bilateral confidence interval= [0.0420159, 7.51437]
beta= 0.95
Unilateral confidence interval (lower tail)= [-3.20963, 6.45529]
beta= 0.95
Unilateral confidence interval (upper tail)= [0.354217, 50.3543]
beta= 0.95
mean= [2.86582]
standard deviation= [1.92382]
skewness= [1.13955]
kurtosis= [5.4]
covariance= [[ 3.7011 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[mu : 2, sigma : 1.5, xi : 0]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [0.577216]
standard moment n= 2 , value= [1.97811]
standard moment n= 3 , value= [5.44487]
standard moment n= 4 , value= [23.5615]
standard moment n= 5 , value= [117.839]
Standard representative= Gumbel(alpha = 1, beta = 0)
mu= 2.0
sigma= 1.5
xi= 0.0
Actual distribution= Gumbel(alpha = 0.666667, beta = 2)
Distribution from actual distribution= GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0)
##################################################
Distribution  GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0.15)
Elliptical =  False
Continuous =  True
oneRealization= [-0.353173]
oneSample first= [1.54401]  last= [7.90517]
mean= [3.13554]
covariance= [[ 5.80678 ]]
Kolmogorov test for the generator, sample size= 100  is  True
Kolmogorov test for the generator, sample size= 10000  is  True
Point=  [1.0]
ddf     = [0.127801]
ddf (FD)= 0.12780130326
log pdf= -1.61629961231
pdf     = 0.198632357566
pdf (FD)= 0.198632357558
cdf= 0.132841517691
ccdf= 0.867158482309
survival= 0.867158482309
Inverse survival= [0.482513]
Survival(inverse survival)= 0.95
pdf gradient     = [0.00847762,-0.134884,-0.127801]
pdf gradient (FD)= [-0.127801,-0.0472207,0.095424]
cdf gradient     = [-0.0282528,-0.178769,-0.198632]
cdf gradient (FD)= [-0.198632,0.132422,-0.0685353]
quantile= [7.61316]
cdf(quantile)= 0.95
Minimum volume interval= [-0.261956, 7.81353]
threshold= 0.95
Minimum volume level set= {x | f(x) <= 3.47643e+56} with f=
MinimumVolumeLevelSetEvaluation(GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0.15))
beta= 0.0
Bilateral confidence interval= [0.22178, 9.35746]
beta= 0.95
Unilateral confidence interval (lower tail)= [-8, 7.61316]
beta= 0.95
Unilateral confidence interval (upper tail)= [0.482513, 1251.08]
beta= 0.95
mean= [3.12484]
standard deviation= [2.45836]
skewness= [2.53025]
kurtosis= [19.2742]
covariance= [[ 6.04353 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[mu : 2, sigma : 1.5, xi : 0.15]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [1.11248]
standard moment n= 2 , value= [1.29806]
standard moment n= 3 , value= [1.61612]
standard moment n= 4 , value= [2.21815]
standard moment n= 5 , value= [3.62435]
Standard representative= Frechet(alpha = 6.66667, beta = 1, gamma = 0)
mu= 2.0
sigma= 1.5
xi= 0.15
Actual distribution= Frechet(alpha = 6.66667, beta = 10, gamma = -8)
Distribution from actual distribution= GeneralizedExtremeValue(mu=2, sigma=1.5, xi=0.15)
