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#! /usr/bin/env python
from __future__ import print_function
from openturns import *
TESTPREAMBLE()
RandomGenerator.SetSeed(0)
try:
# Instanciate one distribution object
distribution = Student(6.5, -0.5, 2.0)
print("Distribution ", repr(distribution))
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=", repr(oneRealization))
# Test for sampling
size = 10000
oneSample = distribution.getSample(size)
print("oneSample first=", repr(
oneSample[0]), " last=", repr(oneSample[size - 1]))
print("mean=", repr(oneSample.computeMean()))
print("covariance=", repr(oneSample.computeCovariance()))
size = 100
for i in range(2):
msg = ''
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(), 1.0)
print("Point= ", repr(point))
# Show PDF and CDF of point
eps = 1e-5
# derivative of PDF with regards its arguments
DDF = distribution.computeDDF(point)
print("ddf =", repr(DDF))
# by the finite difference technique
print("ddf (FD)=", repr(NumericalPoint(1, (distribution.computePDF(
point + NumericalPoint(1, eps)) - distribution.computePDF(point + NumericalPoint(1, -eps))) / (2.0 * eps))))
# PDF value
LPDF = distribution.computeLogPDF(point)
print("log pdf=%.6f" % LPDF)
PDF = distribution.computePDF(point)
print("pdf =%.6f" % PDF)
# by the finite difference technique from CDF
print("pdf (FD)=%.6f" % ((distribution.computeCDF(point + NumericalPoint(1, eps)) -
distribution.computeCDF(point + NumericalPoint(1, -eps))) / (2.0 * eps)))
# derivative of the PDF with regards the parameters of the distribution
CDF = distribution.computeCDF(point)
print("cdf=%.6f" % CDF)
CCDF = distribution.computeComplementaryCDF(point)
print("ccdf=%.6f" % CCDF)
PDFgr = distribution.computePDFGradient(point)
print("pdf gradient =", repr(PDFgr))
# by the finite difference technique
PDFgrFD = NumericalPoint(3)
PDFgrFD[0] = (Student(distribution.getNu() + eps, distribution.getMu(), distribution.getSigma()[0]).computePDF(point) -
Student(distribution.getNu() - eps, distribution.getMu(), distribution.getSigma()[0]).computePDF(point)) / (2.0 * eps)
PDFgrFD[1] = (Student(distribution.getNu(), distribution.getMu() + eps, distribution.getSigma()[0]).computePDF(point) -
Student(distribution.getNu(), distribution.getMu() - eps, distribution.getSigma()[0]).computePDF(point)) / (2.0 * eps)
PDFgrFD[2] = (Student(distribution.getNu(), distribution.getMu(), distribution.getSigma()[0] + eps).computePDF(point) -
Student(distribution.getNu(), distribution.getMu(), distribution.getSigma()[0] - eps).computePDF(point)) / (2.0 * eps)
print("pdf gradient (FD)=", repr(PDFgrFD))
# derivative of the PDF with regards the parameters of the distribution
CDFgr = distribution.computeCDFGradient(point)
print("cdf gradient =", repr(CDFgr))
CDFgrFD = NumericalPoint(3)
CDFgrFD[0] = (Student(distribution.getNu() + eps, distribution.getMu(), distribution.getSigma()[0]).computeCDF(point) -
Student(distribution.getNu() - eps, distribution.getMu(), distribution.getSigma()[0]).computeCDF(point)) / (2.0 * eps)
CDFgrFD[1] = (Student(distribution.getNu(), distribution.getMu() + eps, distribution.getSigma()[0]).computeCDF(point) -
Student(distribution.getNu(), distribution.getMu() - eps, distribution.getSigma()[0]).computeCDF(point)) / (2.0 * eps)
CDFgrFD[2] = (Student(distribution.getNu(), distribution.getMu(), distribution.getSigma()[0] + eps).computeCDF(point) -
Student(distribution.getNu(), distribution.getMu(), distribution.getSigma()[0] - eps).computeCDF(point)) / (2.0 * eps)
print("cdf gradient (FD)=", repr(CDFgrFD))
# quantile
quantile = distribution.computeQuantile(0.95)
print("quantile=", repr(quantile))
print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile))
mean = distribution.getMean()
print("mean=", repr(mean))
standardDeviation = distribution.getStandardDeviation()
print("standard deviation=", repr(standardDeviation))
skewness = distribution.getSkewness()
print("skewness=", repr(skewness))
kurtosis = distribution.getKurtosis()
print("kurtosis=", repr(kurtosis))
covariance = distribution.getCovariance()
print("covariance=", repr(covariance))
parameters = distribution.getParametersCollection()
print("parameters=", repr(parameters))
for i in range(6):
print("standard moment n=", i, " value=",
distribution.getStandardMoment(i))
print("Standard representative=", distribution.getStandardRepresentative())
# Specific to this distribution
beta = point.normSquare()
densityGenerator = distribution.computeDensityGenerator(beta)
print("density generator=%.6f" % densityGenerator)
print("pdf via density generator=%.6f" %
EllipticalDistribution.computePDF(distribution, point))
densityGeneratorDerivative = distribution.computeDensityGeneratorDerivative(
beta)
print("density generator derivative =%.6f" %
densityGeneratorDerivative)
print("density generator derivative (FD)=%.6f" % ((distribution.computeDensityGenerator(
beta + eps) - distribution.computeDensityGenerator(beta - eps)) / (2.0 * eps)))
densityGeneratorSecondDerivative = distribution.computeDensityGeneratorSecondDerivative(
beta)
print("density generator second derivative =%.6f" %
densityGeneratorSecondDerivative)
print("density generator second derivative (FD)=%.6f" % ((distribution.computeDensityGeneratorDerivative(
beta + eps) - distribution.computeDensityGeneratorDerivative(beta - eps)) / (2.0 * eps)))
except:
import sys
print("t_Student_std.py", sys.exc_info()[0], sys.exc_info()[1])
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