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
87
88
89
90
91
92
93
94
95
96
97
98
|
#! /usr/bin/env python
from __future__ import print_function
from openturns import *
from math import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
# Instanciate one distribution object
dim = 2
copula = ClaytonCopula(2.5)
print("Copula ", repr(copula))
print("Copula ", copula)
print("Mean ", repr(copula.getMean()))
print("Covariance ", repr(copula.getCovariance()))
# Is this copula an elliptical distribution?
print("Elliptical distribution= ", copula.isElliptical())
# Is this copula elliptical ?
print("Elliptical copula= ", copula.hasEllipticalCopula())
# Is this copula independent ?
print("Independent copula= ", copula.hasIndependentCopula())
# Test for realization of distribution
oneRealization = copula.getRealization()
print("oneRealization=", repr(oneRealization))
# Test for sampling
size = 10
oneSample = copula.getSample(size)
print("oneSample=", repr(oneSample))
# Test for sampling
size = 10000
anotherSample = copula.getSample(size)
print("anotherSample mean=", repr(anotherSample.computeMean()))
print("anotherSample covariance=", repr(anotherSample.computeCovariance()))
# Define a point
point = NumericalPoint(dim, 0.2)
# Show PDF and CDF of point
pointPDF = copula.computePDF(point)
pointCDF = copula.computeCDF(point)
print("Point = ", repr(point), " pdf=%.6f" %
pointPDF, " cdf=%.6f" % pointCDF)
# Get 50% quantile
quantile = copula.computeQuantile(0.5)
print("Quantile=", repr(quantile))
print("CDF(quantile)=%.6f" % copula.computeCDF(quantile))
# Extract the marginals
for i in range(dim):
margin = copula.getMarginal(i)
print("margin=", repr(margin))
print("margin PDF=%.6f" % margin.computePDF(NumericalPoint(1, 0.25)))
print("margin CDF=%.6f" % margin.computeCDF(NumericalPoint(1, 0.25)))
print("margin quantile=", repr(margin.computeQuantile(0.95)))
print("margin realization=", repr(margin.getRealization()))
# Extract a 2-D marginal
indices = Indices(2, 0)
indices[0] = 1
indices[1] = 0
print("indices=", repr(indices))
margins = copula.getMarginal(indices)
print("margins=", repr(margins))
print("margins PDF=%.6f" % margins.computePDF(NumericalPoint(2, 0.25)))
print("margins CDF=%.6f" % margins.computeCDF(NumericalPoint(2, 0.25)))
quantile = NumericalPoint(margins.computeQuantile(0.95))
print("margins quantile=", repr(quantile))
print("margins CDF(qantile)=%.6f" % margins.computeCDF(quantile))
print("margins realization=", repr(margins.getRealization()))
# Additional tests for PDF/CDF in extreme cases
# We focus on the main diagonal as it is the most challenging computation
points = [[1.0e-12] * 2, [1.0e-7] * 2, [0.1] * 2,
[0.5] * 2, [0.1] * 2, [0.1] * 2, [0.1] * 2]
thetas = [1.0e-12, 0.9e-8, 1.1e-8, -0.99, 9.9e1, 1.1e2, 1.0e5]
c_py = list()
C_py = list()
for i in range(len(thetas)):
x = NumericalPoint(points[i])
copula = ClaytonCopula(thetas[i])
print(copula)
c_py.append(copula.computePDF(x))
C_py.append(copula.computeCDF(x))
print("PDF(", x, ")=%.12e" % c_py[i])
print("CDF(", x, ")=%.12e" % C_py[i])
except:
import sys
print("t_ClaytonCopula_std.py", sys.exc_info()[0], sys.exc_info()[1])
|
