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Parameters collection= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1]]
Standard representative= Normal(mu = 0, sigma = 1)
Distribution class=Normal name=A normal distribution 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)
Covariance class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
Elliptical = True
Continuous = True
oneRealization= class=Point name=Unnamed dimension=1 values=[0.6082]
Point= class=Point name=Unnamed dimension=1 values=[0.5]
ddf = class=Point name=Unnamed dimension=1 values=[-0.17603]
log pdf=-1.043939
pdf =0.352065
characteristic function=0.882497+0.000000i
log characteristic function=-0.125000+0.000000i
cdf=0.691462
ccdf=0.308538
pdf gradient = class=Point name=Unnamed dimension=2 values=[0.17603,-0.26405]
quantile= class=Point name=Unnamed dimension=1 values=[1.6449]
cdf(quantile)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-1.6449]
Survival(inverseSurvival)=0.950000
entropy=1.418939
Minimum volume interval= [-1.96, 1.96]
threshold= [0.95]
Minimum volume level set= {x | f(x) <= 2.8397} with f=
MinimumVolumeLevelSetEvaluation(Normal(mu = 0, sigma = 1))
beta= [0.058445]
Bilateral confidence interval= [-1.96, 1.96]
beta= [0.95]
Unilateral confidence interval (lower tail)= [-7.6506, 1.6449]
beta= [0.95]
Unilateral confidence interval (upper tail)= [-1.6449, 7.6506]
beta= [0.95]
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]
roughness=0.282095
covariance= class=CovarianceMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
parameters= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1]]
density generator=0.352065
pdf via density generator=0.352065
density generator derivative =-0.176033
density generator derivative (FD)=-0.176033
density generator second derivative =0.088016
density generator second derivative (FD)=0.088016
Radial CDF(2.000000 )=0.954500
conditional PDF=0.333225
conditional CDF=0.725747
conditional quantile=0.253347
sequential conditional PDF= [0.35207]
sequential conditional CDF( [1.5] )= [0.93319]
sequential conditional quantile( [0.93319] )= [1.5]
margin= class=Normal name=A normal distribution 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=0.352065
margin CDF=0.691462
margin quantile= class=Point name=Unnamed dimension=1 values=[1.6449]
margin realization= class=Point name=Unnamed dimension=1 values=[-1.2662]
chol= class=TriangularMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
chol*t(chol)= class=SquareMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
Parameters collection= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=dependence dimension=1 description=[R_1_0] values=[0.5]]
Standard representative= Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
[ 0 1 ]])
Distribution class=Normal name=A normal distribution 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 ]])
Covariance class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,1,4]
Elliptical = True
Continuous = True
oneRealization= class=Point name=Unnamed dimension=2 values=[0.94754,0.51137]
Point= class=Point name=Unnamed dimension=2 values=[0.5,0.5]
ddf = class=Point name=Unnamed dimension=2 values=[-0.040546,0]
log pdf=-2.512183
pdf =0.081091
characteristic function=0.416862+0.000000i
log characteristic function=-0.875000+0.000000i
cdf=0.486770
ccdf=0.513230
pdf gradient = class=Point name=Unnamed dimension=5 values=[0.040546,-0.060818,0,-0.040546,0.054061]
quantile= class=Point name=Unnamed dimension=2 values=[1.9163,3.8327]
cdf(quantile)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=2 values=[-1.9163,-3.8327]
Survival(inverseSurvival)=0.950000
entropy=3.387183
Minimum volume interval= [-2.2121, 2.2121]
[-4.4243, 4.4243]
threshold= [0.97304]
Minimum volume level set= {x | f(x) <= 5.3829} with f=
MinimumVolumeLevelSetEvaluation(Normal(mu = [0,0], sigma = [1,2], R = [[ 1 0.5 ]
[ 0.5 1 ]]))
beta= [0.0045944]
Bilateral confidence interval= [-2.2121, 2.2121]
[-4.4243, 4.4243]
beta= [0.97304]
Unilateral confidence interval (lower tail)= [-7.6506, 1.9163]
[-15.301, 3.8327]
beta= [0.97234]
Unilateral confidence interval (upper tail)= [-1.9163, 7.6506]
[-3.8327, 15.301]
beta= [0.97234]
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]
roughness=0.045944
covariance= class=CovarianceMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,1,4]
parameters= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=dependence dimension=1 description=[R_1_0] values=[0.5]]
density generator=0.123950
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(2.000000 )=0.864665
conditional PDF=0.224268
conditional CDF=0.591319
conditional quantile=0.638810
sequential conditional PDF= [0.35207,0.23033]
sequential conditional CDF( [1.5,2.5] )= [0.93319,0.71815]
sequential conditional quantile( [0.93319,0.71815] )= [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=0.352065
margin CDF=0.691462
margin quantile= class=Point name=Unnamed dimension=1 values=[1.6449]
margin realization= class=Point name=Unnamed dimension=1 values=[0.28384]
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=0.193334
margin CDF=0.598706
margin quantile= class=Point name=Unnamed dimension=1 values=[3.2897]
margin realization= class=Point name=Unnamed dimension=1 values=[0.10592]
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=0.486770
margins quantile= class=Point name=Unnamed dimension=2 values=[3.8327,1.9163]
margins CDF(qantile)=0.950000
margins realization= class=Point name=Unnamed dimension=2 values=[0.64156,-0.3331]
chol= class=TriangularMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,0,1.7321]
chol*t(chol)= class=SquareMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,1,1,4]
Parameters collection= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=Marginal 3 dimension=2 description=[mu_2,sigma_2] values=[0,3],class=PointWithDescription name=dependence dimension=3 description=[R_1_0,R_2_0,R_2_1] values=[0.5,0,0.5]]
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=A normal distribution 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 ]])
Covariance class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,1,4,3,0,3,9]
Elliptical = True
Continuous = True
oneRealization= class=Point name=Unnamed dimension=3 values=[0.24358,-1.0577,0.85407]
Point= class=Point name=Unnamed dimension=3 values=[0.5,0.5,0.5]
ddf = class=Point name=Unnamed dimension=3 values=[-0.0075453,0.0010779,-0.0010779]
log pdf=-4.347835
pdf =0.012935
characteristic function=0.063928+0.000000i
log characteristic function=-2.750000+0.000000i
cdf=0.329811
ccdf=0.670189
pdf gradient = class=Point name=Unnamed dimension=9 values=[0.0075453,-0.0091621,-0.0010779,-0.0067369,0.0010779,-0.0041319,0.011677,-0.0045811,0.012396]
quantile= class=Point name=Unnamed dimension=3 values=[2.0798,4.1596,6.2395]
cdf(quantile)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=3 values=[-2.0798,-4.1596,-6.2395]
Survival(inverseSurvival)=0.950000
entropy=5.702001
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]
roughness=0.005291
covariance= class=CovarianceMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,1,4,3,0,3,9]
parameters= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=Marginal 3 dimension=2 description=[mu_2,sigma_2] values=[0,3],class=PointWithDescription name=dependence dimension=3 description=[R_1_0,R_2_0,R_2_1] values=[0.5,0,0.5]]
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 =0.010910
density generator second derivative (FD)=0.010910
Radial CDF(2.000000 )=0.738536
conditional PDF=0.158054
conditional CDF=0.596752
conditional quantile=0.620571
sequential conditional PDF= [0.35207,0.23033,0.15951]
sequential conditional CDF( [1.5,2.5,3.5] )= [0.93319,0.71815,0.84628]
sequential conditional quantile( [0.93319,0.71815,0.84628] )= [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=0.352065
margin CDF=0.691462
margin quantile= class=Point name=Unnamed dimension=1 values=[1.6449]
margin realization= class=Point name=Unnamed dimension=1 values=[-1.1276]
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=0.193334
margin CDF=0.598706
margin quantile= class=Point name=Unnamed dimension=1 values=[3.2897]
margin realization= class=Point name=Unnamed dimension=1 values=[-2.5256]
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=0.131147
margin CDF=0.566184
margin quantile= class=Point name=Unnamed dimension=1 values=[4.9346]
margin realization= class=Point name=Unnamed dimension=1 values=[4.3802]
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=0.486770
margins quantile= class=Point name=Unnamed dimension=2 values=[3.8327,1.9163]
margins CDF(qantile)=0.950000
margins realization= class=Point name=Unnamed dimension=2 values=[-3.2404,-0.11209]
chol= class=TriangularMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,0,1.7321,1.7321,0,0,2.4495]
chol*t(chol)= class=SquareMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,1,0,1,4,3,0,3,9]
Parameters collection= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=Marginal 3 dimension=2 description=[mu_2,sigma_2] values=[0,3],class=PointWithDescription name=Marginal 4 dimension=2 description=[mu_3,sigma_3] values=[0,4],class=PointWithDescription name=dependence dimension=6 description=[R_1_0,R_2_0,R_2_1,R_3_0,R_3_1,R_3_2] values=[0.5,0,0.5,0,0,0.5]]
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=A normal distribution 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 ]])
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]
Elliptical = True
Continuous = True
oneRealization= class=Point name=Unnamed dimension=4 values=[2.0738,3.3102,-1.8095,-4.8331]
Point= class=Point name=Unnamed dimension=4 values=[0.5,0.5,0.5,0.5]
ddf = class=Point name=Unnamed dimension=4 values=[-0.00095189,0.00013598,-0.00013598,0]
log pdf=-6.418066
pdf =0.001632
characteristic function=0.001930+0.000000i
log characteristic function=-6.250000+0.000000i
cdf=0.221454
ccdf=0.778546
pdf gradient = class=Point name=Unnamed dimension=14 values=[0.00095189,-0.0011559,-0.00013598,-0.0008499,0.00013598,-0.00052127,0,-0.00040795,0.0017995,-0.0010675,0.0025429,0.00065272,-0.0013054,0.0019582]
entropy=8.272233
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]
roughness=0.000472
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]
parameters= [class=PointWithDescription name=Marginal 1 dimension=2 description=[mu_0,sigma_0] values=[0,1],class=PointWithDescription name=Marginal 2 dimension=2 description=[mu_1,sigma_1] values=[0,2],class=PointWithDescription name=Marginal 3 dimension=2 description=[mu_2,sigma_2] values=[0,3],class=PointWithDescription name=Marginal 4 dimension=2 description=[mu_3,sigma_3] values=[0,4],class=PointWithDescription name=dependence dimension=6 description=[R_1_0,R_2_0,R_2_1,R_3_0,R_3_1,R_3_2] values=[0.5,0,0.5,0,0,0.5]]
density generator=0.015364
pdf via density generator=0.001632
density generator derivative =-0.007682
density generator derivative (FD)=-0.007682
density generator second derivative =0.003841
density generator second derivative (FD)=0.003841
Radial CDF(2.000000 )=0.593994
conditional PDF=0.125151
conditional CDF=0.550328
conditional quantile=1.001154
sequential conditional PDF= [0.35207,0.23033,0.15951,0.12616]
sequential conditional CDF( [1.5,2.5,3.5,4.5] )= [0.93319,0.71815,0.84628,0.73646]
sequential conditional quantile( [0.93319,0.71815,0.84628,0.73646] )= [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=0.352065
margin CDF=0.691462
margin quantile= class=Point name=Unnamed dimension=1 values=[1.6449]
margin realization= class=Point name=Unnamed dimension=1 values=[0.50866]
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=0.193334
margin CDF=0.598706
margin quantile= class=Point name=Unnamed dimension=1 values=[3.2897]
margin realization= class=Point name=Unnamed dimension=1 values=[-1.0222]
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=0.131147
margin CDF=0.566184
margin quantile= class=Point name=Unnamed dimension=1 values=[4.9346]
margin realization= class=Point name=Unnamed dimension=1 values=[1.1037]
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=0.549738
margin quantile= class=Point name=Unnamed dimension=1 values=[6.5794]
margin realization= class=Point name=Unnamed dimension=1 values=[1.2777]
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=0.486770
margins quantile= class=Point name=Unnamed dimension=2 values=[3.8327,1.9163]
margins CDF(qantile)=0.950000
margins realization= class=Point name=Unnamed dimension=2 values=[-2.0688,-0.087266]
chol= class=TriangularMatrix dimension=4 implementation=class=MatrixImplementation name=Unnamed rows=4 columns=4 values=[1,1,0,0,0,1.7321,1.7321,0,0,0,2.4495,2.4495,0,0,0,3.1623]
chol*t(chol)= class=SquareMatrix 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]
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