Distribution class=GeneralizedPareto name=GeneralizedPareto dimension=1 sigma=1.5 xi=-0.2
Distribution GeneralizedPareto(sigma = 1.5, xi=-0.2)
Elliptical = false
Continuous = true
oneRealization=class=Point name=Unnamed dimension=1 values=[0.662264]
oneSample first=class=Point name=Unnamed dimension=1 values=[0.184665] last=class=Point name=Unnamed dimension=1 values=[1.18051]
mean=class=Point name=Unnamed dimension=1 values=[1.24428]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1.12783]
Kolmogorov test for the generator, sample size=100 is accepted
Kolmogorov test for the generator, sample size=1000 is accepted
Point= class=Point name=Unnamed dimension=1 values=[1]
ddf     =class=Point name=Unnamed dimension=1 values=[-0.231453]
ddf (FD)=class=Point name=Unnamed dimension=1 values=[-0.231453]
log pdf=-0.977868
pdf     =0.376112
pdf (FD)=0.376112
cdf=0.511054
ccdf=0.488946
survival=0.488946
Inverse survival=class=Point name=Unnamed dimension=1 values=[0.0765466]
Survival(inverse survival)=0.95
characteristic function=(0.322373,0.527748)
log characteristic function=(-0.480588,1.02244)
pdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.096439,-0.188281]
pdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.096439,-0.188281]
cdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.250741,-0.131347]
cdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.250741,-0.131347]
quantile=class=Point name=Unnamed dimension=1 values=[3.3804]
cdf(quantile)=0.95
Minimum volume interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[3.3804] finite lower bound=[1] finite upper bound=[1]
threshold=0.95
Minimum volume level set=class=LevelSet name=Unnamed dimension=1 function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[x0,y0] evaluationImplementation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=-0.2)) gradientImplementation=MinimumVolumeLevelSetGradient(GeneralizedPareto(sigma = 1.5, xi=-0.2)) hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=1 values=[0.0001] evaluation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=-0.2)) level=2.80205
beta=0.0606855
Bilateral confidence interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.0378807] upper bound=class=Point name=Unnamed dimension=1 values=[3.91368] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (lower tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[3.3804] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (upper tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.0765466] upper bound=class=Point name=Unnamed dimension=1 values=[7.5] finite lower bound=[1] finite upper bound=[1]
beta=0.95
mean=class=Point name=Unnamed dimension=1 values=[1.25]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1.11607]
correlation=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
spearman=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
kendall=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
parameters=[[sigma : 1.5, xi : -0.2]]
standard moment n=0, value=class=Point name=Unnamed dimension=1 values=[1]
standard moment n=1, value=class=Point name=Unnamed dimension=1 values=[0.833333]
standard moment n=2, value=class=Point name=Unnamed dimension=1 values=[1.19048]
standard moment n=3, value=class=Point name=Unnamed dimension=1 values=[2.23214]
standard moment n=4, value=class=Point name=Unnamed dimension=1 values=[4.96032]
standard moment n=5, value=class=Point name=Unnamed dimension=1 values=[12.4008]
Standard representative=GeneralizedPareto(sigma = 1, xi=-0.2)
standard deviation=class=Point name=Unnamed dimension=1 values=[1.05644]
skewness=class=Point name=Unnamed dimension=1 values=[1.18322]
kurtosis=class=Point name=Unnamed dimension=1 values=[4.2]
sigma=1.5
xi=-0.2
Distribution class=GeneralizedPareto name=GeneralizedPareto dimension=1 sigma=1.5 xi=0
Distribution GeneralizedPareto(sigma = 1.5, xi=0)
Elliptical = false
Continuous = true
oneRealization=class=Point name=Unnamed dimension=1 values=[0.115607]
oneSample first=class=Point name=Unnamed dimension=1 values=[2.83459] last=class=Point name=Unnamed dimension=1 values=[5.88096]
mean=class=Point name=Unnamed dimension=1 values=[1.4961]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[2.26942]
Kolmogorov test for the generator, sample size=100 is accepted
Kolmogorov test for the generator, sample size=1000 is accepted
Point= class=Point name=Unnamed dimension=1 values=[1]
ddf     =class=Point name=Unnamed dimension=1 values=[-0.114093]
ddf (FD)=class=Point name=Unnamed dimension=1 values=[-0.228185]
log pdf=-1.07213
pdf     =0.342278
pdf (FD)=0.342278
cdf=0.486583
ccdf=0.513417
survival=0.513417
Inverse survival=class=Point name=Unnamed dimension=1 values=[0.0769399]
Survival(inverse survival)=0.95
characteristic function=(0.5,0.5)
log characteristic function=(-0.346574,0.785398)
pdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.0760618,-0.152124]
pdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.0760618,-0.152124]
cdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.228185,-0.114093]
cdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.228185,-0.114093]
quantile=class=Point name=Unnamed dimension=1 values=[4.4936]
cdf(quantile)=0.95
Minimum volume interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[4.4936] finite lower bound=[1] finite upper bound=[1]
threshold=0.95
Minimum volume level set=class=LevelSet name=Unnamed dimension=1 function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[x0,y0] evaluationImplementation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=0)) gradientImplementation=MinimumVolumeLevelSetGradient(GeneralizedPareto(sigma = 1.5, xi=0)) hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=1 values=[0.0001] evaluation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=0)) level=3.4012
beta=0.0333333
Bilateral confidence interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.0379767] upper bound=class=Point name=Unnamed dimension=1 values=[5.53332] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (lower tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[4.4936] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (upper tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.0769399] upper bound=class=Point name=Unnamed dimension=1 values=[54.0655] finite lower bound=[1] finite upper bound=[1]
beta=0.95
mean=class=Point name=Unnamed dimension=1 values=[1.5]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[2.25]
correlation=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
spearman=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
kendall=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
parameters=[[sigma : 1.5, xi : 0]]
standard moment n=0, value=class=Point name=Unnamed dimension=1 values=[1]
standard moment n=1, value=class=Point name=Unnamed dimension=1 values=[1]
standard moment n=2, value=class=Point name=Unnamed dimension=1 values=[2]
standard moment n=3, value=class=Point name=Unnamed dimension=1 values=[6]
standard moment n=4, value=class=Point name=Unnamed dimension=1 values=[24]
standard moment n=5, value=class=Point name=Unnamed dimension=1 values=[120]
Standard representative=GeneralizedPareto(sigma = 1, xi=0)
standard deviation=class=Point name=Unnamed dimension=1 values=[1.5]
skewness=class=Point name=Unnamed dimension=1 values=[2]
kurtosis=class=Point name=Unnamed dimension=1 values=[9]
sigma=1.5
xi=0
Distribution class=GeneralizedPareto name=GeneralizedPareto dimension=1 sigma=1.5 xi=0.2
Distribution GeneralizedPareto(sigma = 1.5, xi=0.2)
Elliptical = false
Continuous = true
oneRealization=class=Point name=Unnamed dimension=1 values=[0.116502]
oneSample first=class=Point name=Unnamed dimension=1 values=[3.44463] last=class=Point name=Unnamed dimension=1 values=[8.92872]
mean=class=Point name=Unnamed dimension=1 values=[1.87267]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[6.01684]
Kolmogorov test for the generator, sample size=100 is accepted
Kolmogorov test for the generator, sample size=1000 is accepted
Point= class=Point name=Unnamed dimension=1 values=[1]
ddf     =class=Point name=Unnamed dimension=1 values=[-0.222073]
ddf (FD)=class=Point name=Unnamed dimension=1 values=[-0.222073]
log pdf=-1.15644
pdf     =0.314603
pdf (FD)=0.314603
cdf=0.465175
ccdf=0.534825
survival=0.534825
Inverse survival=class=Point name=Unnamed dimension=1 values=[0.0773359]
Survival(inverse survival)=0.95
characteristic function=(0.298705,0.418886)
log characteristic function=(-0.664599,0.951337)
pdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.0616868,-0.125946]
pdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.0616868,-0.125946]
cdf gradient     =class=Point name=Unnamed dimension=2 values=[-0.209735,-0.100495]
cdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[-0.209735,-0.100495]
quantile=class=Point name=Unnamed dimension=1 values=[6.15423]
cdf(quantile)=0.95
Minimum volume interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[6.15423] finite lower bound=[1] finite upper bound=[1]
threshold=0.95
Minimum volume level set=class=LevelSet name=Unnamed dimension=1 function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[x0,y0] evaluationImplementation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=0.2)) gradientImplementation=MinimumVolumeLevelSetGradient(GeneralizedPareto(sigma = 1.5, xi=0.2)) hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=1 values=[0.0001] evaluation=MinimumVolumeLevelSetEvaluation(GeneralizedPareto(sigma = 1.5, xi=0.2)) level=4.00034
beta=0.0183093
Bilateral confidence interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.038073] upper bound=class=Point name=Unnamed dimension=1 values=[8.18459] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (lower tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0] upper bound=class=Point name=Unnamed dimension=1 values=[6.15423] finite lower bound=[1] finite upper bound=[1]
beta=0.95
Unilateral confidence interval (upper tail)=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[0.0773359] upper bound=class=Point name=Unnamed dimension=1 values=[10126.3] finite lower bound=[1] finite upper bound=[1]
beta=0.95
mean=class=Point name=Unnamed dimension=1 values=[1.875]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[5.85938]
correlation=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
spearman=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
kendall=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
parameters=[[sigma : 1.5, xi : 0.2]]
standard moment n=0, value=class=Point name=Unnamed dimension=1 values=[1]
standard moment n=1, value=class=Point name=Unnamed dimension=1 values=[1.25]
standard moment n=2, value=class=Point name=Unnamed dimension=1 values=[4.16667]
standard moment n=3, value=class=Point name=Unnamed dimension=1 values=[31.25]
standard moment n=4, value=class=Point name=Unnamed dimension=1 values=[625]
NotDefinedException : Error: the standard moments are defined up to order 5 and n=5
Standard representative=GeneralizedPareto(sigma = 1, xi=0.2)
standard deviation=class=Point name=Unnamed dimension=1 values=[2.42061]
skewness=class=Point name=Unnamed dimension=1 values=[4.64758]
kurtosis=class=Point name=Unnamed dimension=1 values=[73.8]
sigma=1.5
xi=0.2
