testCases= [[class=Uniform name=Uniform dimension=1 a=-1 b=3,class=Uniform name=Uniform dimension=1 a=-1 b=3], [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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] 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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[-2] 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]], [class=Exponential name=Exponential dimension=1 lambda=1 gamma=0,class=Exponential name=Exponential dimension=1 lambda=1 gamma=0,class=Exponential name=Exponential dimension=1 lambda=1 gamma=0]]
references= [Triangular(a = -2, m = 2, b = 6),Normal(mu = -1, sigma = 3),Gamma(k = 3, lambda = 1, gamma = 0)]
Distribution  class=RandomMixture name=RandomMixture distribution collection=[class=Uniform name=Uniform dimension=1 a=-1 b=3,class=Uniform name=Uniform dimension=1 a=-1 b=3] weights =class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=2 values=[1,1] constant=class=Point name=Unnamed dimension=1 values=[0]
Distribution  RandomMixture(Uniform(a = -1, b = 3) + Uniform(a = -1, b = 3))
Elliptical =  True
Continuous =  True
oneRealization= [4.05073]
oneSample first= [0.455382]  last= [-0.838226]
mean= [2.01098]
covariance= [[ 2.67867 ]]
Point=  [0.5]
ddf      =0.0625
ddf (ref)= [0.0625]
pdf      =0.156250
pdf  (FD)=0.156250
pdf (ref)=0.156250
cdf      =0.195313
cdf (ref)=0.195312
characteristic function=0.382574 + 0.595823i
log characteristic function=-0.345207 + 1.000000i
quantile      = [4.73509]
quantile (ref)= [4.73509]
cdf(quantile)=0.950000
quantile comp.= [-0.735089]
cdfComp(quantileComp)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-0.735089]
Survival(inverseSurvival)=0.950000
mean      = [2]
mean (ref)= [2]
standard deviation      = [1.63299]
standard deviation (ref)= [1.63299]
skewness      = [0]
skewness (ref)= [0]
kurtosis      = [2.4]
kurtosis (ref)= [2.4]
covariance      = [[ 2.66667 ]]
covariance (ref)= [[ 2.66667 ]]
parameters= [[Uniform_a : -1, Uniform_b : 3, Uniform_a : -1, Uniform_b : 3]]
Standard representative= RandomMixture(Uniform(a = -1, b = 3) + Uniform(a = -1, b = 3))
blockMin= 5
blockMax= 20
maxSize= 4000000
alpha= 5.0
beta= 8.5
Distribution  class=RandomMixture name=RandomMixture distribution collection=[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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] 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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[-2] 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]] weights =class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=3 values=[1,1,1] constant=class=Point name=Unnamed dimension=1 values=[0]
Distribution  RandomMixture(Normal(mu = 0, sigma = 1) + Normal(mu = 1, sigma = 2) + Normal(mu = -2, sigma = 2))
Elliptical =  True
Continuous =  True
oneRealization= [2.57239]
oneSample first= [-7.73611]  last= [0.219605]
mean= [-1.00692]
covariance= [[ 9.14206 ]]
Point=  [0.5]
ddf      =-0.019559
ddf (ref)= [-0.0195592]
pdf      =0.117355
pdf  (FD)=0.117355
pdf (ref)=0.117355
cdf      =0.691462
cdf (ref)=0.691462
characteristic function=0.284909 + -0.155647i
log characteristic function=-1.125000 + -0.500000i
quantile      = [3.93456]
quantile (ref)= [3.93456]
cdf(quantile)=0.950000
quantile comp.= [-5.93456]
cdfComp(quantileComp)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=1 values=[-5.93456]
Survival(inverseSurvival)=0.950000
mean      = [-1]
mean (ref)= [-1]
standard deviation      = [3]
standard deviation (ref)= [3]
skewness      = [0]
skewness (ref)= [0]
kurtosis      = [3]
kurtosis (ref)= [3]
covariance      = [[ 9 ]]
covariance (ref)= [[ 9 ]]
parameters= [[Normal_mean_0 : 0, Normal_standard_deviation_0 : 1, Normal_mean_0 : 1, Normal_standard_deviation_0 : 2, Normal_mean_0 : -2, Normal_standard_deviation_0 : 2]]
Standard representative= RandomMixture(Normal(mu = 0, sigma = 1) + Normal(mu = 1, sigma = 2) + Normal(mu = -2, sigma = 2))
blockMin= 5
blockMax= 20
maxSize= 4000000
alpha= 5.0
beta= 8.5
Distribution  class=RandomMixture name=RandomMixture distribution collection=[class=Exponential name=Exponential dimension=1 lambda=1 gamma=0,class=Exponential name=Exponential dimension=1 lambda=1 gamma=0,class=Exponential name=Exponential dimension=1 lambda=1 gamma=0] weights =class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=3 values=[1,1,1] constant=class=Point name=Unnamed dimension=1 values=[0]
Distribution  RandomMixture(Exponential(lambda = 1, gamma = 0) + Exponential(lambda = 1, gamma = 0) + Exponential(lambda = 1, gamma = 0))
Elliptical =  False
Continuous =  True
oneRealization= [2.3902]
oneSample first= [1.80165]  last= [5.94924]
mean= [3.00598]
covariance= [[ 3.02995 ]]
Point=  [0.5]
ddf      =0.22745
ddf (ref)= [0.227449]
pdf      =0.075816
pdf  (FD)=0.075816
pdf (ref)=0.075816
cdf      =0.014388
cdf (ref)=0.014388
characteristic function=0.128000 + 0.704000i
log characteristic function=-0.334715 + 1.390943i
quantile      = [6.2957]
quantile (ref)= [6.29579]
cdf(quantile)=0.950000
quantile comp.= [0.817691]
cdfComp(quantileComp)=0.950000
InverseSurvival= class=Point name=Unnamed dimension=1 values=[0.817691]
Survival(inverseSurvival)=0.950000
mean      = [3]
mean (ref)= [3]
standard deviation      = [1.73205]
standard deviation (ref)= [1.73205]
skewness      = [1.1547]
skewness (ref)= [1.1547]
kurtosis      = [5]
kurtosis (ref)= [5]
covariance      = [[ 3 ]]
covariance (ref)= [[ 3 ]]
parameters= [[Exponential_lambda : 1, Exponential_gamma : 0, Exponential_lambda : 1, Exponential_gamma : 0, Exponential_lambda : 1, Exponential_gamma : 0]]
Standard representative= RandomMixture(Exponential(lambda = 1, gamma = 0) + Exponential(lambda = 1, gamma = 0) + Exponential(lambda = 1, gamma = 0))
blockMin= 5
blockMax= 20
maxSize= 4000000
alpha= 5.0
beta= 8.5
distribution= class=RandomMixture name=RandomMixture distribution collection=[class=Dirac name=Dirac dimension=1 point=class=Point name=Unnamed dimension=1 values=[0.5],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] 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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[2] 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],class=Uniform name=Uniform dimension=1 a=-2 b=2,class=Uniform name=Uniform dimension=1 a=2 b=4,class=Exponential name=Exponential dimension=1 lambda=2 gamma=-3,class=Dirac name=Dirac dimension=1 point=class=Point name=Unnamed dimension=1 values=[0.5],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[1] 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],class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[2] 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],class=Uniform name=Uniform dimension=1 a=-2 b=2,class=Uniform name=Uniform dimension=1 a=2 b=4,class=Exponential name=Exponential dimension=1 lambda=2 gamma=-3,class=Gamma name=Gamma dimension=1 k=3 lambda=4 gamma=-2] weights =class=Matrix implementation=class=MatrixImplementation name=Unnamed rows=1 columns=13 values=[1,2,-3,-1,2,1.5,-2.5,-5,7.5,2.5,-5,-3.75,2.5] constant=class=Point name=Unnamed dimension=1 values=[0]
distribution= RandomMixture(Dirac(point = [0.5]) + 2 * Normal(mu = 1, sigma = 2) - 3 * Normal(mu = 2, sigma = 1) - Uniform(a = -2, b = 2) + 2 * Uniform(a = 2, b = 4) + 1.5 * Exponential(lambda = 2, gamma = -3) - 2.5 * Dirac(point = [0.5]) - 5 * Normal(mu = 1, sigma = 2) + 7.5 * Normal(mu = 2, sigma = 1) + 2.5 * Uniform(a = -2, b = 2) - 5 * Uniform(a = 2, b = 4) - 3.75 * Exponential(lambda = 2, gamma = -3) + 2.5 * Gamma(k = 3, lambda = 4, gamma = -2))
pdf( -45.042123 )=0.000266
pdf( -35.310540 )=0.001666
pdf( -25.578957 )=0.006605
pdf( -15.847374 )=0.016556
pdf( -6.115791 )=0.026232
pdf( 3.615791 )=0.026262
pdf( 13.347374 )=0.016595
pdf( 23.078957 )=0.006608
pdf( 32.810540 )=0.001654
pdf( 42.542123 )=0.000260
projections= [Normal(mu = -1.24816, sigma = 24.4357),Gamma(k = 9.60684, lambda = 0.126843, gamma = -76.9864),Triangular(a = -79.6433, m = -1.2445, b = 77.1434),Uniform(a = -79.6433, b = 77.1434),Exponential(lambda = 0.0132034, gamma = -76.9864)]
norms= [0.125151,0.142711,0.195666,0.299986,0.44751]
distribution =  RandomMixture(
Normal(mu = 0, sigma = 1) - 2 * Normal(mu = 0, sigma = 1) + Normal(mu = 0, sigma = 1)
Normal(mu = 0, sigma = 1) + Normal(mu = 0, sigma = 1) - 3 * Normal(mu = 0, sigma = 1)
)
range =  [-20.8207, 20.8207]
[-28.1913, 28.1913]
mean =  [0,0]
cov =  [[  6 -4 ]
 [ -4 11 ]]
sigma =  [2.44949,3.31662]
pdf      = 0.0225079
pdf (ref)= 0.0225079
pdf      = 0.0139715
pdf (ref)= 0.0139715
pdf      = 0.00334166
pdf (ref)= 0.00334166
pdf      = 0.000307961
pdf (ref)= 0.000307961
pdf      = 1.09356e-05
pdf (ref)= 1.09356e-05
pdf      = 1.49624e-07
pdf (ref)= 1.49624e-07
pdf      = 0.0139715
pdf (ref)= 0.0139715
pdf      = 0.00542272
pdf (ref)= 0.00542272
pdf      = 0.000810972
pdf (ref)= 0.000810972
pdf      = 4.67313e-05
pdf (ref)= 4.67313e-05
pdf      = 1.03758e-06
pdf (ref)= 1.03758e-06
pdf      = 8.8767e-09
pdf (ref)= 8.8767e-09
pdf      = 0.00334166
pdf (ref)= 0.00334166
pdf      = 0.000810972
pdf (ref)= 0.000810972
pdf      = 7.58338e-05
pdf (ref)= 7.58338e-05
pdf      = 2.73233e-06
pdf (ref)= 2.73233e-06
pdf      = 3.7933e-08
pdf (ref)= 3.7933e-08
pdf      = 2.02915e-10
pdf (ref)= 2.02915e-10
pdf      = 0.000307961
pdf (ref)= 0.000307961
pdf      = 4.67313e-05
pdf (ref)= 4.67313e-05
pdf      = 2.73233e-06
pdf (ref)= 2.73233e-06
pdf      = 6.15563e-08
pdf (ref)= 6.15563e-08
pdf      = 5.34349e-10
pdf (ref)= 5.34349e-10
pdf      = 1.78727e-12
pdf (ref)= 1.78727e-12
pdf      = 1.09356e-05
pdf (ref)= 1.09356e-05
pdf      = 1.03758e-06
pdf (ref)= 1.03758e-06
pdf      = 3.7933e-08
pdf (ref)= 3.7933e-08
pdf      = 5.34349e-10
pdf (ref)= 5.34349e-10
pdf      = 2.90032e-12
pdf (ref)= 2.90032e-12
pdf      = 1.49624e-07
pdf (ref)= 1.49624e-07
pdf      = 8.8767e-09
pdf (ref)= 8.8767e-09
pdf      = 2.02915e-10
pdf (ref)= 2.02915e-10
pdf      = 1.78727e-12
pdf (ref)= 1.78727e-12
new distribution =  RandomMixture(
Uniform(a = 0, b = 1) - 2 * Uniform(a = 0, b = 1) + Uniform(a = 0, b = 1)
Uniform(a = 0, b = 1) + Uniform(a = 0, b = 1) - 3 * Uniform(a = 0, b = 1)
)
range =  [-2, 2]
[-3, 2]
mean =  [0,-0.5]
cov =  [[  0.5      -0.333333 ]
 [ -0.333333  0.916667 ]]
sigma =  [0.707107,0.957427]
pdf      = 0.200008
pdf      = 0.199953
pdf      = 0.18257
pdf      = 0.161365
pdf      = 0.140147
pdf      = 0.11893
pdf      = 0.200012
pdf      = 0.194237
pdf      = 0.172999
pdf      = 0.151788
pdf      = 0.130572
pdf      = 0.109357
pdf      = 0.200032
pdf      = 0.184647
pdf      = 0.163427
pdf      = 0.142211
pdf      = 0.120996
pdf      = 0.099784
pdf      = 0.190057
pdf      = 0.175051
pdf      = 0.153858
pdf      = 0.132633
pdf      = 0.111423
pdf      = 0.0902108
pdf      = 0.164538
pdf      = 0.155122
pdf      = 0.144316
pdf      = 0.123061
pdf      = 0.101846
pdf      = 0.0806394
pdf      = 0.13901
pdf      = 0.129584
pdf      = 0.120154
pdf      = 0.110695
pdf      = 0.0922665
pdf      = 0.0710676
3D distribution =  RandomMixture(
Normal(mu = 0, sigma = 1) - 0.05 * Mixture((w = 0.5, d = Normal(mu = 2, sigma = 1)), (w = 0.5, d = Normal(mu = -2, sigma = 1))) + Uniform(a = 0, b = 1) - 0.5 * Uniform(a = 0, b = 1)
0.5 * Normal(mu = 0, sigma = 1) + Mixture((w = 0.5, d = Normal(mu = 2, sigma = 1)), (w = 0.5, d = Normal(mu = -2, sigma = 1))) - 0.05 * Uniform(a = 0, b = 1) + 0.3 * Uniform(a = 0, b = 1)
-0.5 * Normal(mu = 0, sigma = 1) - 0.1 * Mixture((w = 0.5, d = Normal(mu = 2, sigma = 1)), (w = 0.5, d = Normal(mu = -2, sigma = 1))) + 1.2 * Uniform(a = 0, b = 1) - 0.8 * Uniform(a = 0, b = 1)
)
range =  [-8.63316, 9.13316]
[-13.5259, 13.7759]
[-5.59038, 5.99038]
mean =  [0.25,0.125,0.2]
cov =  [[  1.11667   0.233333 -0.341667 ]
 [  0.233333  5.25771  -0.775    ]
 [ -0.341667 -0.775     0.473333 ]]
sigma =  [1.05672,2.29297,0.687992]
pdf      = 0.0128814
pdf      = 0.0128655
pdf      = 0.0122294
pdf      = 0.00984818
pdf      = 0.0234842
pdf      = 0.020225
pdf      = 0.0150424
pdf      = 0.00949663
pdf      = 0.0432697
pdf      = 0.0385232
pdf      = 0.0281784
pdf      = 0.0180749
pdf      = 0.044762
pdf      = 0.0406428
pdf      = 0.0308978
pdf      = 0.0210441
pdf      = 0.0129975
pdf      = 0.0121201
pdf      = 0.00968603
pdf      = 0.0071769
pdf      = 0.0247237
pdf      = 0.0192342
pdf      = 0.0131031
pdf      = 0.00795833
pdf      = 0.0400697
pdf      = 0.0318194
pdf      = 0.0226119
pdf      = 0.0136759
pdf      = 0.0348167
pdf      = 0.0294142
pdf      = 0.0218493
pdf      = 0.0134862
pdf      = 0.011291
pdf      = 0.0091266
pdf      = 0.00689789
pdf      = 0.00454873
pdf      = 0.0207392
pdf      = 0.0154986
pdf      = 0.00997757
pdf      = 0.00537413
pdf      = 0.0295955
pdf      = 0.0230235
pdf      = 0.0149557
pdf      = 0.00725254
pdf      = 0.0229623
pdf      = 0.0183174
pdf      = 0.0117906
pdf      = 0.00422686
pdf      = 0.00832467
pdf      = 0.00628249
pdf      = 0.00406557
pdf      = 0.00186481
pdf      = 0.0152402
pdf      = 0.0104641
pdf      = 0.00556431
pdf      = 0.00128214
pdf      = 0.0189734
pdf      = 0.0129675
pdf      = 0.00534378
pdf      = 0.000220278
pdf      = 0.0123168
pdf      = 0.00770527
pdf      = 0.00160947
pdf      = 0
case 1, q=0.384146
case 1, q comp=0.000393
case 2, q=-0.000393
case 2, q comp=-0.384146
