1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
Point= [0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3]
ddf = [-0.000319153,-0.000319153,-0.000370522,-0.000346163,-0.000389754,-0.000368254,-0.000368254]
ddf (ref)= [-0.000319153,-0.000319153,-0.000370522,-0.000346163,-0.000389754,-0.000368254,-0.000368254]
pdf =0.00160
pdf (ref)=0.00160
cdf =0.05406
cdf (ref)=0.05406
Survival =0.00350
Survival (ref)=0.00350
Inverse survival = [-2.43216,-2.43216,-2.43216,-2.43216,-2.43216,-2.43216,-2.43216]
Inverse survival (ref)= [-2.43216,-2.43216,-2.43216,-2.43216,-2.43216,-2.43216,-2.43216]
Survival(inverse survival)=0.95000
Quantile = [1.26874,1.26874,1.26874,1.26874,1.26874,1.26874,1.26874]
Quantile (ref)= [1.26874,1.26874,1.26874,1.26874,1.26874,1.26874,1.26874]
CDF(quantile) =0.50000
Distribution BlockIndependentDistribution(JointDistribution(Normal(mu = 0, sigma = 1), Normal(mu = 0, sigma = 1), AliMikhailHaqCopula(theta = 0.5)), Normal(mu = [1,1,1], sigma = [2,2,2], R = [[ 1 0.5 0.25 ]
[ 0.5 1 0 ]
[ 0.25 0 1 ]]), JointDistribution(Exponential(lambda = 1, gamma = 0), Exponential(lambda = 1, gamma = 0), FrankCopula(theta = 0.5)))
Elliptical distribution= False
Continuous = True
Elliptical = False
Independent = False
oneRealization= [-0.877312,-0.87746,0.69751,2.27139,2.52837,0.152066,1.60952]
Point= [0.3, 0.3, 0.3, 0.3, 0.3, 0.3, 0.3]
ddf = [-0.000161544,-0.000161544,4.80573e-05,0.000108129,0.000120143,-0.000877177,-0.000877177]
pdf =0.00076
cdf=0.00284
Survival =0.03219
Survival (ref)=0.03219
Inverse survival= [-2.4345,-2.4345,-3.869,-3.869,-3.869,0.0074841,0.0074841]
Survival(inverse survival)=0.95000
Quantile= [1.28123,1.28123,3.56246,3.56246,3.56246,2.30202,2.30202]
CDF(quantile)=0.50000
entropy =10.96404
standard deviation= class=Point name=Unnamed dimension=7 values=[1,1,2,2,2,1,1]
kurtosis= class=Point name=Unnamed dimension=7 values=[3,3,3,3,3,9,9]
conditional PDF=0.55675
conditional CDF=0.49062
conditional quantile=0.82304
sequential conditional PDF= [0.398444,0.407104,0.185928,0.227445,0.203657,0.57695,0.525447]
sequential conditional CDF( [0.05,0.15,0.25,0.35,0.45,0.55,0.65] )= [0.519939,0.545655,0.35383,0.436925,0.415568,0.42305,0.487447]
sequential conditional quantile( [0.519939,0.545655,0.35383,0.436925,0.415568,0.42305,0.487447] )= [0.05,0.15,0.25,0.35,0.45,0.55,0.65]
indices= [1, 2, 3, 5, 6]
margins= BlockIndependentDistribution(Normal(mu = 0, sigma = 1), Normal(mu = [1,1], sigma = [2,2], R = [[ 1 0.5 ]
[ 0.5 1 ]]), JointDistribution(Exponential(lambda = 1, gamma = 0), Exponential(lambda = 1, gamma = 0), FrankCopula(theta = 0.5)))
margins PDF=0.01057
margins CDF=0.00675
margins quantile= [2.30912,5.61824,5.61824,4.55939,4.55939]
margins CDF(quantile)=0.95000
margins realization= [-0.42058,2.80782,6.41388,0.234171,0.323429]
isoprobabilistic transformation (general normal)= [((RosenblattEvaluation(AliMikhailHaqCopula(theta = 0.5)->Normal(2))o(| y0 = Normal(mu = 0, sigma = 1) -> y0 : Uniform(a = 0, b = 1)
| y1 = Normal(mu = 0, sigma = 1) -> y1 : Uniform(a = 0, b = 1)
))o([x0,x1,x2,x3,x4,x5,x6]->[x0,x1]),(RosenblattEvaluation(Normal(mu = [1,1,1], sigma = [2,2,2], R = [[ 1 0.5 0.25 ]
[ 0.5 1 0 ]
[ 0.25 0 1 ]])->Normal(3))o([x0,x1,x2,x3,x4,x5,x6]->[x2,x3,x4]),((RosenblattEvaluation(FrankCopula(theta = 0.5)->Normal(2))o(| y0 = Exponential(lambda = 1, gamma = 0) -> y0 : Uniform(a = 0, b = 1)
| y1 = Exponential(lambda = 1, gamma = 0) -> y1 : Uniform(a = 0, b = 1)
))o([x0,x1,x2,x3,x4,x5,x6]->[x5,x6])]
isoprobabilistic transformation (general non-normal)= [(RosenblattEvaluation(class=SklarCopula name=SklarCopula dimension=2 distribution=class=Student name=Student dimension=2 nu=3 mean=class=Point name=Unnamed dimension=2 values=[1,1] sigma=class=Point name=Unnamed dimension=2 values=[3,3] correlationMatrix=class=CorrelationMatrix dimension=2 implementation=class=MatrixImplementation name=Unnamed rows=2 columns=2 values=[1,0,0,1]->Normal(2))o([x0,x1,x2,x3,x4,x5,x6,x7]->[x0,x1]),(RosenblattEvaluation(Normal(mu = [1,1,1], sigma = [2,2,2], R = [[ 1 0.5 0.25 ]
[ 0.5 1 0 ]
[ 0.25 0 1 ]])->Normal(3))o([x0,x1,x2,x3,x4,x5,x6,x7]->[x2,x3,x4]),((RosenblattEvaluation(FrankCopula(theta = 0.5)->Normal(2))o(| y0 = Exponential(lambda = 1, gamma = 0) -> y0 : Uniform(a = 0, b = 1)
| y1 = Exponential(lambda = 1, gamma = 0) -> y1 : Uniform(a = 0, b = 1)
))o([x0,x1,x2,x3,x4,x5,x6,x7]->[x5,x6]),(Triangular(a = 2, m = 3, b = 4) -> y0 : Normal(mu = 0, sigma = 1)
)o([x0,x1,x2,x3,x4,x5,x6,x7]->[x7])]
conditional PDF=0.60000
conditional CDF=0.18000
conditional quantile=3.55279
sequential conditional PDF= [1,1.06099,0.185928,0.227445,0.203657,0.57695,0.525447,0]
sequential conditional CDF( [0.05,0.15,0.25,0.35,0.45,0.55,0.65,0.75] )= [0.05,0.220267,0.35383,0.436925,0.415568,0.42305,0.487447,0]
sequential conditional quantile( [0.05,0.220267,0.35383,0.436925,0.415568,0.42305,0.487447,0] )= [0.05,0.15,0.25,0.35,0.45,0.55,0.65,2]
range= [0, 1]
[0, 1]
]-inf (-14.3013), (16.3013) +inf[
]-inf (-14.3013), (16.3013) +inf[
]-inf (-14.3013), (16.3013) +inf[
[0, (32.2362) +inf[
[0, (32.2362) +inf[
[2, 4]
0 : [ 2 2 2 2 ]
1 : [ 3 2 2 2 ]
2 : [ 2 3 2 2 ]
3 : [ 2 2 3 2 ]
4 : [ 3 2 3 2 ]
5 : [ 2 3 3 2 ]
6 : [ 2 2 2 3 ]
7 : [ 3 2 2 3 ]
8 : [ 2 3 2 3 ]
|
