Distribution  Gamma(k = 1.5, lambda = 2.5, gamma = -0.5)
Elliptical =  False
Continuous =  True
oneRealization= [0.281847]
oneSample first= [-0.263977]  last= [-0.375541]
mean= [0.101621]
covariance= [[ 0.247946 ]]
Kolmogorov test for the generator, sample size= 100  is  accepted
Kolmogorov test for the generator, sample size= 1000  is  accepted
Point=  [1]
ddf     = [-0.278355]
ddf (FD)= -0.278355
log pdf= -2.05205
pdf     =0.128471
pdf (FD)=0.128471
cdf= 0.942442
ccdf= 0.0575585
survival= 0.0575585
characteristic function=(0.892418, 0.0632527)
log characteristic function=(-0.111315, 0.0707596)
pdf gradient     = [0.16512,-0.115624,0.278355]
pdf gradient (FD)= [0.16512,-0.115624,0.278355]
cdf gradient     = [-0.0875625,0.0770828,-0.128471]
cdf gradient (FD)= [-0.0875625,0.0770828,-0.128471]
quantile= [1.06295]
cdf(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-0.429631]
Survival(inverseSurvival)=0.950000
Minimum volume interval= [-0.499368, 1.06337]
threshold= [0.95]
Minimum volume level set= {x | f(x) <= 2.18978} with f=
MinimumVolumeLevelSetEvaluation(Gamma(k = 1.5, lambda = 2.5, gamma = -0.5))
beta= [0.111942]
Bilateral confidence interval= [-0.456841, 1.36968]
beta= [0.95]
Unilateral confidence interval (lower tail)= [-0.5, 1.06295]
beta= [0.95]
Unilateral confidence interval (upper tail)= [-0.429631, 13.1546]
beta= [0.95]
mean= [0.1]
covariance= [[ 0.24 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[k : 1.5, lambda : 2.5, gamma : -0.5]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [1.5]
standard moment n= 2 , value= [3.75]
standard moment n= 3 , value= [13.125]
standard moment n= 4 , value= [59.0625]
standard moment n= 5 , value= [324.844]
Standard representative= Gamma(k = 1.5, lambda = 1, gamma = 0)
standard deviation= [0.489898]
skewness= [1.63299]
kurtosis= [7]
Distribution  Gamma(k = 15, lambda = 2.5, gamma = 0)
Elliptical =  False
Continuous =  True
oneRealization= [6.03324]
oneSample first= [4.73401]  last= [3.93099]
mean= [6.02305]
covariance= [[ 2.44857 ]]
Kolmogorov test for the generator, sample size= 100  is  accepted
Kolmogorov test for the generator, sample size= 1000  is  accepted
Point=  [1]
ddf     = [1.00845e-05]
ddf (FD)= 1.00845e-05
log pdf= -13.9469
pdf     =8.76911e-07
pdf (FD)=8.76911e-07
cdf= 6.91531e-08
ccdf= 1
survival= 1
characteristic function=(0.275588, -0.178824)
log characteristic function=(-1.11315, 5.7076)
pdf gradient     = [-1.54166e-06,4.38456e-06,-1.00845e-05]
pdf gradient (FD)= [-1.54166e-06,4.38456e-06,-1.00845e-05]
cdf gradient     = [-1.26959e-07,3.50764e-07,-8.76911e-07]
cdf gradient (FD)= [-1.26959e-07,3.50764e-07,-8.76911e-07]
quantile= [8.75459]
cdf(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[3.69853]
Survival(inverseSurvival)=0.950000
Minimum volume interval= [3.1431, 9.09027]
threshold= [0.95]
Minimum volume level set= {x | f(x) <= 3.27167} with f=
MinimumVolumeLevelSetEvaluation(Gamma(k = 15, lambda = 2.5, gamma = 0))
beta= [0.037943]
Bilateral confidence interval= [3.35815, 9.39585]
beta= [0.95]
Unilateral confidence interval (lower tail)= [0, 8.75459]
beta= [0.95]
Unilateral confidence interval (upper tail)= [3.69853, 26.3665]
beta= [0.95]
mean= [6]
covariance= [[ 2.4 ]]
correlation= [[ 1 ]]
spearman= [[ 1 ]]
kendall= [[ 1 ]]
parameters= [[k : 15, lambda : 2.5, gamma : 0]]
standard moment n= 0 , value= [1]
standard moment n= 1 , value= [15]
standard moment n= 2 , value= [240]
standard moment n= 3 , value= [4080]
standard moment n= 4 , value= [73440]
standard moment n= 5 , value= [1.39536e+06]
Standard representative= Gamma(k = 15, lambda = 1, gamma = 0)
standard deviation= [1.54919]
skewness= [0.516398]
kurtosis= [3.4]
