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##################################################
method= GaussProduct
distribution= CompoundDistribution(X with X|Theta~JointDistribution(Theta), Theta=f(Y), f=id_4, Y~JointDistribution(Dirac(point = [1]), Dirac(point = [2]), Bernoulli(p = 0.7), Uniform(a = 3, b = 4), IndependentCopula(dimension = 4)))
Parameters [[point_0_marginal_0 : 1],[point_0_marginal_1 : 2],[p_marginal_2 : 0.7],[a_marginal_3 : 3, b_marginal_3 : 4],[]]
Mean [1.5,2.1]
Elliptical distribution= False
Elliptical copula= False
Independent copula= False
oneRealization= [1.13528,1.0937]
oneSample= [ X0 X1 ]
0 : [ 1.92068 2.49374 ]
1 : [ 1.71438 1.87896 ]
2 : [ 1.8835 1.80748 ]
3 : [ 1.68457 3.16374 ]
4 : [ 1.58862 1.53788 ]
5 : [ 1.21044 2.02765 ]
6 : [ 1.98184 3.21605 ]
7 : [ 1.25986 2.2968 ]
8 : [ 1.11108 1.85243 ]
9 : [ 1.97898 2.729 ]
anotherSample mean= [1.50538,2.09375]
anotherSample covariance= [[ 0.0847776 -0.000929088 ]
[ -0.000929088 0.74965 ]]
Zero point= [0,0] pdf= 0.0 cdf= 0.0
Quantile= [1.97468,3.60358]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=2 values=[1.02532,0.293386]
Survival(inverseSurvival)=0.950000
Unilateral confidence interval (lower tail)= [-1, 1.97468]
[-1, 3.60358]
beta= [0.974679]
Unilateral confidence interval (upper tail)= [1.02532, 1]
[0.293386, 1]
beta= [0.974679]
##################################################
method= QMC
distribution= CompoundDistribution(X with X|Theta~JointDistribution(Theta), Theta=f(Y), f=id_4, Y~JointDistribution(Dirac(point = [1]), Dirac(point = [2]), Bernoulli(p = 0.7), Uniform(a = 3, b = 4), IndependentCopula(dimension = 4)))
Parameters [[point_0_marginal_0 : 1],[point_0_marginal_1 : 2],[p_marginal_2 : 0.7],[a_marginal_3 : 3, b_marginal_3 : 4],[]]
Mean [1.5,2.09997]
Elliptical distribution= False
Elliptical copula= False
Independent copula= False
oneRealization= [1.28994,2.70175]
oneSample= [ X0 X1 ]
0 : [ 1.724 1.349 ]
1 : [ 1.08472 3.51038 ]
2 : [ 1.46333 2.69445 ]
3 : [ 1.84205 2.68757 ]
4 : [ 1.88905 2.07805 ]
5 : [ 1.61304 0.0419325 ]
6 : [ 1.87194 0.394497 ]
7 : [ 1.34017 2.39098 ]
8 : [ 1.88327 2.3063 ]
9 : [ 1.41826 2.7288 ]
anotherSample mean= [1.50033,2.09473]
anotherSample covariance= [[ 0.0823686 9.04142e-05 ]
[ 9.04142e-05 0.756718 ]]
Zero point= [0,0] pdf= 0.0 cdf= 0.0
Quantile= [1.97468,3.60334]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=2 values=[1.02532,0.293381]
Survival(inverseSurvival)=0.950000
Unilateral confidence interval (lower tail)= [-1, 1.97468]
[-1, 3.60334]
beta= [0.974679]
Unilateral confidence interval (upper tail)= [1.02532, 1]
[0.293381, 1]
beta= [0.974679]
##################################################
method= MC
distribution= CompoundDistribution(X with X|Theta~JointDistribution(Theta), Theta=f(Y), f=id_4, Y~JointDistribution(Dirac(point = [1]), Dirac(point = [2]), Bernoulli(p = 0.7), Uniform(a = 3, b = 4), IndependentCopula(dimension = 4)))
Parameters [[point_0_marginal_0 : 1],[point_0_marginal_1 : 2],[p_marginal_2 : 0.7],[a_marginal_3 : 3, b_marginal_3 : 4],[]]
Mean [1.5,2.10103]
Elliptical distribution= False
Elliptical copula= False
Independent copula= False
oneRealization= [1.25105,2.80837]
oneSample= [ X0 X1 ]
0 : [ 1.31227 1.91181 ]
1 : [ 1.85168 1.81568 ]
2 : [ 1.78838 2.33992 ]
3 : [ 1.52819 3.33285 ]
4 : [ 1.89918 2.42515 ]
5 : [ 1.41437 3.33561 ]
6 : [ 1.46582 2.14057 ]
7 : [ 1.71435 2.49255 ]
8 : [ 1.61359 3.09347 ]
9 : [ 1.87601 1.21486 ]
anotherSample mean= [1.49875,2.10847]
anotherSample covariance= [[ 0.0835088 0.002056 ]
[ 0.002056 0.748267 ]]
Zero point= [0,0] pdf= 0.0 cdf= 0.0
Quantile= [1.97468,3.60826]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=2 values=[1.02532,0.293522]
Survival(inverseSurvival)=0.950000
Unilateral confidence interval (lower tail)= [-1, 1.97468]
[-1, 3.60826]
beta= [0.974679]
Unilateral confidence interval (upper tail)= [1.02532, 1]
[0.293522, 1]
beta= [0.974679]
conditioning distribution= JointDistribution(Uniform(a = 0, b = 1), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2))
Distribution CompoundDistribution(X with X|Theta~Normal(Theta), Theta=f(Y), f=id_2, Y~JointDistribution(Uniform(a = 0, b = 1), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2)))
Parameters [[a_marginal_0 : 0, b_marginal_0 : 1],[a_marginal_1 : 1, b_marginal_1 : 2],[]]
Mean [0.49998]
Covariance [[ 2.42797 ]]
Elliptical distribution= False
Elliptical copula= True
Independent copula= True
oneRealization= [1.35735]
oneSample= [ X0 ]
0 : [ 2.15156 ]
1 : [ -0.0274854 ]
2 : [ -0.515759 ]
3 : [ 1.33154 ]
4 : [ 3.43509 ]
5 : [ 1.21906 ]
6 : [ 2.84108 ]
7 : [ 3.32709 ]
8 : [ -1.93128 ]
9 : [ 1.0006 ]
anotherSample mean= [0.493427]
anotherSample covariance= [[ 2.39148 ]]
Zero point= [0] pdf=0.253294 cdf=0.368038
Quantile= [3.05746]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-2.05552]
Survival(inverseSurvival)=0.950000
conditioning distribution= JointDistribution(Binomial(n = 3, p = 0.5), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2))
Distribution CompoundDistribution(X with X|Theta~Normal(Theta), Theta=f(Y), f=id_2, Y~JointDistribution(Binomial(n = 3, p = 0.5), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2)))
Parameters [[n_marginal_0 : 3, p_marginal_0 : 0.5],[a_marginal_1 : 1, b_marginal_1 : 2],[]]
Mean [1.5]
Covariance [[ 3.09555 ]]
Elliptical distribution= False
Elliptical copula= True
Independent copula= True
oneRealization= [3.73237]
oneSample= [ X0 ]
0 : [ -0.678003 ]
1 : [ 0.129661 ]
2 : [ 3.15535 ]
3 : [ 1.10271 ]
4 : [ 0.417401 ]
5 : [ 2.75515 ]
6 : [ 2.09963 ]
7 : [ -1.09533 ]
8 : [ 4.28327 ]
9 : [ -2.47362 ]
anotherSample mean= [1.50548]
anotherSample covariance= [[ 3.0539 ]]
Zero point= [0] pdf=0.156662 cdf=0.192661
Quantile= [4.38606]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-1.38606]
Survival(inverseSurvival)=0.950000
conditioning distribution= JointDistribution(Dirac(point = [0.5]), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2))
Distribution CompoundDistribution(X with X|Theta~Normal(Theta), Theta=f(Y), f=id_2, Y~JointDistribution(Dirac(point = [0.5]), Uniform(a = 1, b = 2), IndependentCopula(dimension = 2)))
Parameters [[point_0_marginal_0 : 0.5],[a_marginal_1 : 1, b_marginal_1 : 2],[]]
Mean [0.5]
Covariance [[ 2.33541 ]]
Elliptical distribution= False
Elliptical copula= True
Independent copula= True
oneRealization= [1.58198]
oneSample= [ X0 ]
0 : [ 1.62667 ]
1 : [ -1.68229 ]
2 : [ 4.89959 ]
3 : [ 1.72367 ]
4 : [ -1.13326 ]
5 : [ 0.177625 ]
6 : [ 1.46685 ]
7 : [ 0.59936 ]
8 : [ 1.59169 ]
9 : [ -0.94916 ]
anotherSample mean= [0.52044]
anotherSample covariance= [[ 2.34821 ]]
Zero point= [0] pdf=0.258471 cdf=0.364815
Quantile= [3.00756]
CDF(quantile)= 0.95
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-2.00756]
Survival(inverseSurvival)=0.950000
|
