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|
*** Case 1 ***
Parameters collection=[[mu_0 : 0, sigma_0 : 1]]
Standard representative=Normal(mu = 0, sigma = 1)
Distribution class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
Distribution Normal(mu = 0, sigma = 1)
Elliptical = true
Continuous = true
oneRealization=class=Point name=Unnamed dimension=1 values=[0.608202]
oneSample first=class=Point name=Unnamed dimension=1 values=[-1.26617] last=class=Point name=Unnamed dimension=1 values=[1.5244]
mean=class=Point name=Unnamed dimension=1 values=[-0.0132171]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1.0005]
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=[0.5]
ddf =class=Point name=Unnamed dimension=1 values=[-0.176033]
log pdf=-1.0439
pdf =0.35207
pdf (FD)=0.35207
cdf=0.69146
ccdf=0.30854
survival=0.30854
Inverse survival=class=Point name=Unnamed dimension=1 values=[-1.64485]
Survival(inverse survival)=0.95
characteristic function=(0.8825,0)
log characteristic function=(-0.125,0)
pdf gradient =class=Point name=Unnamed dimension=2 values=[0.176033,-0.264049]
pdf gradient (FD)=class=Point name=Unnamed dimension=2 values=[0.176033,-0.264049]
cdf gradient =class=Point name=Unnamed dimension=2 values=[-0.352065,-0.176033]
quantile=class=Point name=Unnamed dimension=1 values=[1.645]
cdf(quantile)=0.95
Minimum volume interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[-1.95996] upper bound=class=Point name=Unnamed dimension=1 values=[1.95996] 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=[Marginal 1,-logPDF] evaluationImplementation=MinimumVolumeLevelSetEvaluation(Normal(mu = 0, sigma = 1)) gradientImplementation=MinimumVolumeLevelSetGradient(Normal(mu = 0, sigma = 1)) hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=1 values=[0.0001] evaluation=MinimumVolumeLevelSetEvaluation(Normal(mu = 0, sigma = 1)) level=2.83967
beta=0.058445
Bilateral confidence interval=class=Interval name=Unnamed dimension=1 lower bound=class=Point name=Unnamed dimension=1 values=[-1.95996] upper bound=class=Point name=Unnamed dimension=1 values=[1.95996] 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=[-7.65063] upper bound=class=Point name=Unnamed dimension=1 values=[1.64485] 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=[-1.64485] upper bound=class=Point name=Unnamed dimension=1 values=[7.65063] finite lower bound=[1] finite upper bound=[1]
beta=0.95
entropy=1.4189
entropy (MC)=1.4188
mean=class=Point name=Unnamed dimension=1 values=[0]
standard deviation=class=Point name=Unnamed dimension=1 values=[1]
skewness=class=Point name=Unnamed dimension=1 values=[0]
kurtosis=class=Point name=Unnamed dimension=1 values=[3]
covariance=class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
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=[[mu_0 : 0, sigma_0 : 1]]
Standard representative=Normal(mu = 0, sigma = 1)
density generator=0.35207
pdf via density generator=0.35207
density generator derivative =-0.17603
density generator derivative (FD)=-0.17603
density generator second derivative =0.088016
density generator second derivative (FD)=0.088016
Radial CDF(2)=0.9545
conditional PDF=0.33322
conditional CDF=0.72575
conditional quantile=0.25335
sequential conditional PDF=class=Point name=Unnamed dimension=1 values=[0.129518]
sequential conditional CDF(class=Point name=Unnamed dimension=1 values=[1.5])=class=Point name=Unnamed dimension=1 values=[0.933193]
sequential conditional quantile(class=Point name=Unnamed dimension=1 values=[0.933193])=class=Point name=Unnamed dimension=1 values=[1.5]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.35207
margin CDF=0.69146
margin quantile=class=Point name=Unnamed dimension=1 values=[1.64485]
margin realization=class=Point name=Unnamed dimension=1 values=[-0.147003]
chol=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
chol*t(chol)=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
Comparison with a Student distribution false
Comparison with an Exponential distribution false
Comparison with itself true
Comparison with a clone true
Comparison with another member false
*** Case 2 ***
Parameters collection=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[R_1_0 : 0.5]]
Standard representative=Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
[ 0 1 ]])
Distribution class=Normal name=Normal dimension=2 mean=class=Point name=Unnamed dimension=2 values=[0,0] sigma=class=Point name=Unnamed dimension=2 values=[1,2] correlationMatrix=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
Distribution Normal(mu = [0,0], sigma = [1,2], R = [[ 1 0.5 ]
[ 0.5 1 ]])
Elliptical = true
Continuous = true
oneRealization=class=Point name=Unnamed dimension=2 values=[1.10883,-1.07312]
oneSample first=class=Point name=Unnamed dimension=2 values=[-0.667474,-0.628346] last=class=Point name=Unnamed dimension=2 values=[-0.054982,-0.48522]
mean=class=Point name=Unnamed dimension=2 values=[-0.00303261,0.0232072]
covariance=class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1.00407,1.01388,1.01388,4.10035]
Point= class=Point name=Unnamed dimension=2 values=[0.5,0.5]
ddf =class=Point name=Unnamed dimension=2 values=[-0.0405455,0]
log pdf=-2.5122
pdf =0.081091
cdf=0.48677
survival=0.1966
Inverse survival=class=Point name=Unnamed dimension=2 values=[-1.91633,-3.83266]
Survival(inverse survival)=0.95
characteristic function=(0.41686,0)
log characteristic function=(-0.875,0)
pdf gradient =class=Point name=Unnamed dimension=5 values=[0.0405455,-0.0608183,0,-0.0405455,0.0540607]
pdf gradient (FD)=class=Point name=Unnamed dimension=4 values=[0.0405455,0,-0.0608183,-0.0405455]
cdf gradient =class=Point name=Unnamed dimension=5 values=[-0.176033,-0.0880163,-0.12905,-0.0322625,0.162182]
quantile=class=Point name=Unnamed dimension=2 values=[1.916,3.833]
cdf(quantile)=0.95
Minimum volume interval=class=Interval name=Unnamed dimension=2 lower bound=class=Point name=Unnamed dimension=2 values=[-2.21213,-4.42426] upper bound=class=Point name=Unnamed dimension=2 values=[2.21213,4.42426] finite lower bound=[1,1] finite upper bound=[1,1]
threshold=0.97304
Minimum volume level set=class=LevelSet name=Unnamed dimension=2 function=class=Function name=Unnamed implementation=class=FunctionImplementation name=Unnamed description=[Marginal 1,Marginal 2,-logPDF] evaluationImplementation=MinimumVolumeLevelSetEvaluation(Normal(mu = [0,0], sigma = [1,2], R = [[ 1 0.5 ]
[ 0.5 1 ]])) gradientImplementation=MinimumVolumeLevelSetGradient(Normal(mu = [0,0], sigma = [1,2], R = [[ 1 0.5 ]
[ 0.5 1 ]])) hessianImplementation=class=CenteredFiniteDifferenceHessian name=Unnamed epsilon=class=Point name=Unnamed dimension=2 values=[0.0001,0.0001] evaluation=MinimumVolumeLevelSetEvaluation(Normal(mu = [0,0], sigma = [1,2], R = [[ 1 0.5 ]
[ 0.5 1 ]])) level=5.38292
beta=0.0045944
Bilateral confidence interval=class=Interval name=Unnamed dimension=2 lower bound=class=Point name=Unnamed dimension=2 values=[-2.21213,-4.42426] upper bound=class=Point name=Unnamed dimension=2 values=[2.21213,4.42426] finite lower bound=[1,1] finite upper bound=[1,1]
beta=0.97304
Unilateral confidence interval (lower tail)=class=Interval name=Unnamed dimension=2 lower bound=class=Point name=Unnamed dimension=2 values=[-7.65063,-15.3013] upper bound=class=Point name=Unnamed dimension=2 values=[1.91633,3.83266] finite lower bound=[1,1] finite upper bound=[1,1]
beta=0.97234
Unilateral confidence interval (upper tail)=class=Interval name=Unnamed dimension=2 lower bound=class=Point name=Unnamed dimension=2 values=[-1.91633,-3.83266] upper bound=class=Point name=Unnamed dimension=2 values=[7.65063,15.3013] finite lower bound=[1,1] finite upper bound=[1,1]
beta=0.97234
entropy=3.3872
entropy (MC)=3.386
mean=class=Point name=Unnamed dimension=2 values=[0,0]
standard deviation=class=Point name=Unnamed dimension=2 values=[1,2]
skewness=class=Point name=Unnamed dimension=2 values=[0,0]
kurtosis=class=Point name=Unnamed dimension=2 values=[3,3]
covariance=class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,1,4]
correlation=class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
spearman=class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.482584,0.482584,1]
kendall=class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.333333,0.333333,1]
parameters=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[R_1_0 : 0.5]]
Standard representative=Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
[ 0 1 ]])
density generator=0.12395
pdf via density generator=0.081091
density generator derivative =-0.061975
density generator derivative (FD)=-0.061975
density generator second derivative =0.030987
density generator second derivative (FD)=0.030987
Radial CDF(2)=0.86466
conditional PDF=0.22427
conditional CDF=0.59132
conditional quantile=0.63881
sequential conditional PDF=class=Point name=Unnamed dimension=2 values=[0.129518,0.19497]
sequential conditional CDF(class=Point name=Unnamed dimension=2 values=[1.5,2.5])=class=Point name=Unnamed dimension=2 values=[0.933193,0.718149]
sequential conditional quantile(class=Point name=Unnamed dimension=2 values=[0.933193,0.718149])=class=Point name=Unnamed dimension=2 values=[1.5,2.5]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.35207
margin CDF=0.69146
margin quantile=class=Point name=Unnamed dimension=1 values=[1.64485]
margin realization=class=Point name=Unnamed dimension=1 values=[-1.62343]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[2] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.19333
margin CDF=0.59871
margin quantile=class=Point name=Unnamed dimension=1 values=[3.28971]
margin realization=class=Point name=Unnamed dimension=1 values=[-2.18704]
indices=[1,0]
margins=class=Normal name=Normal dimension=2 mean=class=Point name=Unnamed dimension=2 values=[0,0] sigma=class=Point name=Unnamed dimension=2 values=[2,1] correlationMatrix=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
margins PDF=0.081091
margins CDF=0.48677
margins quantile=class=Point name=Unnamed dimension=2 values=[3.83266,1.91633]
margins CDF(quantile)=0.95
margins realization=class=Point name=Unnamed dimension=2 values=[-0.422897,0.902554]
chol=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,0,1.73205]
chol*t(chol)=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,1,4]
Comparison with a Student distribution false
Comparison with an Exponential distribution false
Comparison with itself true
Comparison with a clone true
Comparison with another member false
*** Case 3 ***
Parameters collection=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[mu_2 : 0, sigma_2 : 3],[R_1_0 : 0.5, R_2_0 : 0, R_2_1 : 0.5]]
Standard representative=Normal(mu = [0,0,0], sigma = [1,1,1], R = [[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]])
Distribution class=Normal name=Normal dimension=3 mean=class=Point name=Unnamed dimension=3 values=[0,0,0] sigma=class=Point name=Unnamed dimension=3 values=[1,2,3] correlationMatrix=class=CorrelationMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.5,0,0.5,1,0.5,0,0.5,1]
Distribution Normal(mu = [0,0,0], sigma = [1,2,3], R = [[ 1 0.5 0 ]
[ 0.5 1 0.5 ]
[ 0 0.5 1 ]])
Elliptical = true
Continuous = true
oneRealization=class=Point name=Unnamed dimension=3 values=[-0.245183,0.945252,3.56944]
oneSample first=class=Point name=Unnamed dimension=3 values=[-0.0267208,-1.04332,3.85504] last=class=Point name=Unnamed dimension=3 values=[-0.613991,0.279132,0.114201]
mean=class=Point name=Unnamed dimension=3 values=[-0.000853476,0.00793713,0.00692681]
covariance=class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[0.994158,1.00338,0.0219978,1.00338,4.02393,3.09495,0.0219978,3.09495,9.24621]
Point= class=Point name=Unnamed dimension=3 values=[0.5,0.5,0.5]
ddf =class=Point name=Unnamed dimension=3 values=[-0.00754529,0.0010779,-0.0010779]
log pdf=-4.3478
pdf =0.012935
cdf=0.32981
survival=0.11135
Inverse survival=class=Point name=Unnamed dimension=3 values=[-2.07982,-4.15964,-6.23946]
Survival(inverse survival)=0.95
characteristic function=(0.063928,0)
log characteristic function=(-2.75,0)
pdf gradient =class=Point name=Unnamed dimension=9 values=[0.00754529,-0.00916214,-0.0010779,-0.00673687,0.0010779,-0.00413195,0.0116772,-0.00458107,0.0123958]
pdf gradient (FD)=class=Point name=Unnamed dimension=6 values=[0.00754529,-0.0010779,0.0010779,-0.00916214,-0.00673687,-0.00413195]
cdf gradient =class=Point name=Unnamed dimension=9 values=[-0.133608,-0.0668041,-0.0575624,-0.0143906,-0.0635446,-0.0105908,0.094207,0.0627608,0.121528]
quantile=class=Point name=Unnamed dimension=3 values=[2.08,4.16,6.239]
cdf(quantile)=0.95
entropy=5.702
entropy (MC)=5.7023
mean=class=Point name=Unnamed dimension=3 values=[0,0,0]
standard deviation=class=Point name=Unnamed dimension=3 values=[1,2,3]
skewness=class=Point name=Unnamed dimension=3 values=[0,0,0]
kurtosis=class=Point name=Unnamed dimension=3 values=[3,3,3]
covariance=class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,1,4,3,0,3,9]
correlation=class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.5,0,0.5,1,0.5,0,0.5,1]
spearman=class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.482584,0,0.482584,1,0.482584,0,0.482584,1]
kendall=class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.333333,0,0.333333,1,0.333333,0,0.333333,1]
parameters=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[mu_2 : 0, sigma_2 : 3],[R_1_0 : 0.5, R_2_0 : 0, R_2_1 : 0.5]]
Standard representative=Normal(mu = [0,0,0], sigma = [1,1,1], R = [[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]])
density generator=0.043638
pdf via density generator=0.012935
density generator derivative =-0.021819
density generator derivative (FD)=-0.021819
density generator second derivative =0.01091
density generator second derivative (FD)=0.01091
Radial CDF(2)=0.73854
conditional PDF=0.15805
conditional CDF=0.59675
conditional quantile=0.62057
sequential conditional PDF=class=Point name=Unnamed dimension=3 values=[0.129518,0.19497,0.0967474]
sequential conditional CDF(class=Point name=Unnamed dimension=3 values=[1.5,2.5,3.5])=class=Point name=Unnamed dimension=3 values=[0.933193,0.718149,0.846283]
sequential conditional quantile(class=Point name=Unnamed dimension=3 values=[0.933193,0.718149,0.846283])=class=Point name=Unnamed dimension=3 values=[1.5,2.5,3.5]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.35207
margin CDF=0.69146
margin quantile=class=Point name=Unnamed dimension=1 values=[1.64485]
margin realization=class=Point name=Unnamed dimension=1 values=[-0.0359499]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[2] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.19333
margin CDF=0.59871
margin quantile=class=Point name=Unnamed dimension=1 values=[3.28971]
margin realization=class=Point name=Unnamed dimension=1 values=[-2.53725]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[3] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.13115
margin CDF=0.56618
margin quantile=class=Point name=Unnamed dimension=1 values=[4.93456]
margin realization=class=Point name=Unnamed dimension=1 values=[0.822214]
indices=[1,0]
margins=class=Normal name=Normal dimension=2 mean=class=Point name=Unnamed dimension=2 values=[0,0] sigma=class=Point name=Unnamed dimension=2 values=[2,1] correlationMatrix=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
margins PDF=0.081091
margins CDF=0.48677
margins quantile=class=Point name=Unnamed dimension=2 values=[3.83266,1.91633]
margins CDF(quantile)=0.95
margins realization=class=Point name=Unnamed dimension=2 values=[0.979474,1.35901]
chol=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,0,1.73205,1.73205,0,0,2.44949]
chol*t(chol)=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,1,4,3,0,3,9]
Comparison with a Student distribution false
Comparison with an Exponential distribution false
Comparison with itself true
Comparison with a clone true
Comparison with another member false
*** Case 4 ***
Parameters collection=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[mu_2 : 0, sigma_2 : 3],[mu_3 : 0, sigma_3 : 4],[R_1_0 : 0.5, R_2_0 : 0, R_2_1 : 0.5, R_3_0 : 0, R_3_1 : 0, R_3_2 : 0.5]]
Standard representative=Normal(mu = [0,0,0,0], sigma = [1,1,1,1], R = [[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]])
Distribution class=Normal name=Normal dimension=4 mean=class=Point name=Unnamed dimension=4 values=[0,0,0,0] sigma=class=Point name=Unnamed dimension=4 values=[1,2,3,4] correlationMatrix=class=CorrelationMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,0.5,0,0,0.5,1,0.5,0,0,0.5,1,0.5,0,0,0.5,1]
Distribution Normal(mu = [0,0,0,0], sigma = [1,2,3,4], R = [[ 1 0.5 0 0 ]
[ 0.5 1 0.5 0 ]
[ 0 0.5 1 0.5 ]
[ 0 0 0.5 1 ]])
Elliptical = true
Continuous = true
oneRealization=class=Point name=Unnamed dimension=4 values=[1.29008,-0.0404617,0.42494,4.2962]
oneSample first=class=Point name=Unnamed dimension=4 values=[1.17224,1.62957,-1.99989,-6.8291] last=class=Point name=Unnamed dimension=4 values=[0.367599,2.58853,-0.289899,4.99267]
mean=class=Point name=Unnamed dimension=4 values=[0.0138666,0.0180498,0.0221654,0.0162702]
covariance=class=CovarianceMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[0.970503,0.951581,-0.0277311,-0.0130839,0.951581,3.89801,2.90873,-0.0330447,-0.0277311,2.90873,8.89229,5.93811,-0.0130839,-0.0330447,5.93811,15.6673]
Point= class=Point name=Unnamed dimension=4 values=[0.5,0.5,0.5,0.5]
ddf =class=Point name=Unnamed dimension=4 values=[-0.000951889,0.000135984,-0.000135984,0]
log pdf=-6.4181
pdf =0.0016318
cdf=0.22145
survival=0.067873
characteristic function=(0.0019305,0)
log characteristic function=(-6.25,0)
pdf gradient =class=Point name=Unnamed dimension=14 values=[0.000951889,-0.00115586,-0.000135984,-0.000849901,0.000135984,-0.000521272,0,-0.000407952,0.00179952,-0.00106747,0.0025429,0.000652724,-0.00130545,0.00195817]
pdf gradient (FD)=class=Point name=Unnamed dimension=8 values=[0.000951889,-0.000135984,0.000135984,0,-0.00115586,-0.000849901,-0.000521272,-0.000407952]
entropy=8.2722
entropy (MC)=8.2708
mean=class=Point name=Unnamed dimension=4 values=[0,0,0,0]
standard deviation=class=Point name=Unnamed dimension=4 values=[1,2,3,4]
skewness=class=Point name=Unnamed dimension=4 values=[0,0,0,0]
kurtosis=class=Point name=Unnamed dimension=4 values=[3,3,3,3]
covariance=class=CovarianceMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,1,0,0,1,4,3,0,0,3,9,6,0,0,6,16]
correlation=class=CovarianceMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,0.5,0,0,0.5,1,0.5,0,0,0.5,1,0.5,0,0,0.5,1]
spearman=class=CovarianceMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,0.482584,0,0,0.482584,1,0.482584,0,0,0.482584,1,0.482584,0,0,0.482584,1]
kendall=class=CovarianceMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,0.333333,0,0,0.333333,1,0.333333,0,0,0.333333,1,0.333333,0,0,0.333333,1]
parameters=[[mu_0 : 0, sigma_0 : 1],[mu_1 : 0, sigma_1 : 2],[mu_2 : 0, sigma_2 : 3],[mu_3 : 0, sigma_3 : 4],[R_1_0 : 0.5, R_2_0 : 0, R_2_1 : 0.5, R_3_0 : 0, R_3_1 : 0, R_3_2 : 0.5]]
Standard representative=Normal(mu = [0,0,0,0], sigma = [1,1,1,1], R = [[ 1 0 0 0 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]])
density generator=0.015364
pdf via density generator=0.0016318
density generator derivative =-0.0076818
density generator derivative (FD)=-0.0076818
density generator second derivative =0.0038409
density generator second derivative (FD)=0.0038409
Radial CDF(2)=0.59399
conditional PDF=0.12515
conditional CDF=0.55033
conditional quantile=1.0012
sequential conditional PDF=class=Point name=Unnamed dimension=4 values=[0.129518,0.19497,0.0967474,0.103288]
sequential conditional CDF(class=Point name=Unnamed dimension=4 values=[1.5,2.5,3.5,4.5])=class=Point name=Unnamed dimension=4 values=[0.933193,0.718149,0.846283,0.736455]
sequential conditional quantile(class=Point name=Unnamed dimension=4 values=[0.933193,0.718149,0.846283,0.736455])=class=Point name=Unnamed dimension=4 values=[1.5,2.5,3.5,4.5]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.35207
margin CDF=0.69146
margin quantile=class=Point name=Unnamed dimension=1 values=[1.64485]
margin realization=class=Point name=Unnamed dimension=1 values=[-0.989426]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[2] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.19333
margin CDF=0.59871
margin quantile=class=Point name=Unnamed dimension=1 values=[3.28971]
margin realization=class=Point name=Unnamed dimension=1 values=[-2.65983]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[3] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.13115
margin CDF=0.56618
margin quantile=class=Point name=Unnamed dimension=1 values=[4.93456]
margin realization=class=Point name=Unnamed dimension=1 values=[1.40108]
margin=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[4] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
margin PDF=0.098959
margin CDF=0.54974
margin quantile=class=Point name=Unnamed dimension=1 values=[6.57941]
margin realization=class=Point name=Unnamed dimension=1 values=[7.03462]
indices=[1,0]
margins=class=Normal name=Normal dimension=2 mean=class=Point name=Unnamed dimension=2 values=[0,0] sigma=class=Point name=Unnamed dimension=2 values=[2,1] correlationMatrix=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0.5,0.5,1]
margins PDF=0.081091
margins CDF=0.48677
margins quantile=class=Point name=Unnamed dimension=2 values=[3.83266,1.91633]
margins CDF(quantile)=0.95
margins realization=class=Point name=Unnamed dimension=2 values=[-3.30128,-0.645538]
chol=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,1,0,0,0,1.73205,1.73205,0,0,0,2.44949,2.44949,0,0,0,3.16228]
chol*t(chol)=class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,1,0,0,1,4,3,0,0,3,9,6,0,0,6,16]
Comparison with a Student distribution false
Comparison with an Exponential distribution false
Comparison with itself true
Comparison with a clone true
Comparison with another member false
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