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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
allDistributions = [InverseGamma(5.5, 2.5), InverseGamma(15.0, 2.5)]
for n in range(len(allDistributions)):
distribution = allDistributions[n]
print("Distribution ", distribution)
# Is this distribution elliptical ?
print("Elliptical = ", distribution.isElliptical())
# Is this distribution continuous ?
print("Continuous = ", distribution.isContinuous())
# Test for realization of distribution
oneRealization = distribution.getRealization()
print("oneRealization=", oneRealization)
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", oneSample[0], " last=", oneSample[size - 1])
print("mean=", oneSample.computeMean())
print("covariance=", oneSample.computeCovariance())
size = 100
for i in range(2):
if FittingTest.Kolmogorov(distribution.getSample(size), distribution).getBinaryQualityMeasure():
msg = "accepted"
else:
msg = "rejected"
print(
"Kolmogorov test for the generator, sample size=", size, " is ", msg)
size *= 10
# Define a point
point = NumericalPoint(
distribution.getDimension(), 2.0 / (distribution.getK() * distribution.getLambda()))
print("Point= ", point)
# Show PDF and CDF of point
eps = 1e-5
DDF = distribution.computeDDF(point)
print("ddf =", DDF)
print("ddf (FD)=%.6g" % ((distribution.computePDF(point + NumericalPoint(1, eps)) -
distribution.computePDF(point + NumericalPoint(1, -eps))) / (2.0 * eps)))
LPDF = distribution.computeLogPDF(point)
print("log pdf= %.12g" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6g" % PDF)
print("pdf (FD)=%.6g" % ((distribution.computeCDF(point + NumericalPoint(1, eps)) -
distribution.computeCDF(point + NumericalPoint(1, -eps))) / (2.0 * eps)))
CDF = distribution.computeCDF(point)
print("cdf= %.12g" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf= %.12g" % CCDF)
Survival = distribution.computeSurvivalFunction(point)
print("survival= %.12g" % Survival)
CF = distribution.computeCharacteristicFunction(point[0])
print("characteristic function=(%.6g, %.6g)" % (CF.real, CF.imag))
LCF = distribution.computeLogCharacteristicFunction(point[0])
print("log characteristic function=(%.6g, %.6g)" %
(LCF.real, LCF.imag))
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient =", PDFgr)
PDFgrFD = NumericalPoint(2)
PDFgrFD[0] = (InverseGamma(distribution.getK() + eps, distribution.getLambda()).computePDF(point) -
InverseGamma(distribution.getK() - eps, distribution.getLambda()).computePDF(point)) / (2.0 * eps)
PDFgrFD[1] = (InverseGamma(distribution.getK(), distribution.getLambda() + eps).computePDF(point) -
InverseGamma(distribution.getK(), distribution.getLambda() - eps).computePDF(point)) / (2.0 * eps)
print("pdf gradient (FD)=", PDFgrFD)
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient =", CDFgr)
CDFgrFD = NumericalPoint(2)
CDFgrFD[0] = (InverseGamma(distribution.getK() + eps, distribution.getLambda()).computeCDF(point) -
InverseGamma(distribution.getK() - eps, distribution.getLambda()).computeCDF(point)) / (2.0 * eps)
CDFgrFD[1] = (InverseGamma(distribution.getK(), distribution.getLambda() + eps).computeCDF(point) -
InverseGamma(distribution.getK(), distribution.getLambda() - eps).computeCDF(point)) / (2.0 * eps)
print("cdf gradient (FD)=", CDFgrFD)
quantile = distribution.computeQuantile(0.95)
print("quantile=", quantile)
print("cdf(quantile)= %.2f" % distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", mean)
covariance = distribution.getCovariance()
print("covariance=", covariance)
correlation = distribution.getCorrelation()
print("correlation=", correlation)
spearman = distribution.getSpearmanCorrelation()
print("spearman=", spearman)
kendall = distribution.getKendallTau()
print("kendall=", kendall)
parameters = distribution.getParametersCollection()
print("parameters=", parameters)
for i in range(6):
print("standard moment n=", i, ", value=",
distribution.getStandardMoment(i))
print("Standard representative=",
distribution.getStandardRepresentative())
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", standardDeviation)
skewness = distribution.getSkewness()
print("skewness=", skewness)
kurtosis = distribution.getKurtosis()
print("kurtosis=", kurtosis)
except:
import sys
print("InverseGamma.py", sys.exc_info()[0], sys.exc_info()[1])
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