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Copula OrdinalSumCopula([0, 0.2], FrankCopula(theta = 3), [0.2, 0.7], NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]), [0.7, 1], ClaytonCopula(theta = 2))
Elliptical distribution= False
Continuous = True
Elliptical = False
Independent = False
oneRealization= [0.251363,0.277809]
oneSample first= [0.207289,0.30774] last= [0.506679,0.611576]
mean= [0.502599,0.50222]
covariance= [[ 0.08245 0.076185 ]
[ 0.076185 0.082852 ]]
Point= [0.6, 0.6]
ddf = [5.86093,5.86093]
pdf =2.92442
cdf=0.54358
Survival =0.34358
Survival (ref)=0.34358
Inverse survival= [0.0299408,0.0299408]
Survival(inverse survival)=0.95000
Quantile= [0.567157,0.567157]
CDF(quantile)= 0.5
Minimum volume interval= [0.0135212, 0.986479]
[0.0135212, 0.986479]
threshold=0.97296
Minimum volume level set= {x | f(x) <= -0.21629} with f=
MinimumVolumeLevelSetEvaluation(OrdinalSumCopula([0, 0.2], FrankCopula(theta = 3), [0.2, 0.7], NormalCopula(R = [[ 1 0.5 ]
[ 0.5 1 ]]), [0.7, 1], ClaytonCopula(theta = 2)))
beta=1.24146
Bilateral confidence interval= [0.0135212, 0.986479]
[0.0135212, 0.986479]
beta=0.97296
Unilateral confidence interval (lower tail)= [0, 0.971607]
[0, 0.971607]
beta=0.97161
Unilateral confidence interval (upper tail)= [0.0299408, 1]
[0.0299408, 1]
beta=0.97006
entropy=-1.25321
entropy (MC)=-1.25340
mean= [0.5,0.5]
covariance= [[ 0.083333 0.076861 ]
[ 0.076861 0.083333 ]]
correlation= [[ 1 0.92233 ]
[ 0.92233 1 ]]
spearman= [[ 1 0.92233 ]
[ 0.92233 1 ]]
kendall= [[ 1 0.76062 ]
[ 0.76062 1 ]]
parameters= [[theta_copula_0 : 3, R_2_1_copula_1 : 0.5, theta_copula_2 : 2]]
conditional PDF=0.000000
conditional CDF=0.000000
conditional quantile=1.000000
sequential conditional PDF= [1,2.92442]
sequential conditional CDF( [0.05,0.15] )= [0.05,0.883703]
sequential conditional quantile( [0.05,0.883703] )= [0.05,0.15]
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