#! /usr/bin/env python from __future__ import print_function from openturns import * TESTPREAMBLE() RandomGenerator.SetSeed(0) try: # Instanciate one distribution object distribution = Triangular(-0.5, 1.5, 2.5) 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, left part of the support 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) CF = distribution.computeCharacteristicFunction(point[0]) print("characteristic function= (%.12g%+.12gj)" % (CF.real, CF.imag)) PDFgr = distribution.computePDFGradient(point) print("pdf gradient =", repr(PDFgr)) # by the finite difference technique PDFgrFD = NumericalPoint(3) PDFgrFD[0] = (Triangular(distribution.getA() + eps, distribution.getM(), distribution.getB()).computePDF(point) - Triangular(distribution.getA() - eps, distribution.getM(), distribution.getB()).computePDF(point)) / (2.0 * eps) PDFgrFD[1] = (Triangular(distribution.getA(), distribution.getM() + eps, distribution.getB()).computePDF(point) - Triangular(distribution.getA(), distribution.getM() - eps, distribution.getB()).computePDF(point)) / (2.0 * eps) PDFgrFD[2] = (Triangular(distribution.getA(), distribution.getM(), distribution.getB() + eps).computePDF(point) - Triangular(distribution.getA(), distribution.getM(), distribution.getB() - 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] = (Triangular(distribution.getA() + eps, distribution.getM(), distribution.getB()).computeCDF(point) - Triangular(distribution.getA() - eps, distribution.getM(), distribution.getB()).computeCDF(point)) / (2.0 * eps) CDFgrFD[1] = (Triangular(distribution.getA(), distribution.getM() + eps, distribution.getB()).computeCDF(point) - Triangular(distribution.getA(), distribution.getM() - eps, distribution.getB()).computeCDF(point)) / (2.0 * eps) CDFgrFD[2] = (Triangular(distribution.getA(), distribution.getM(), distribution.getB() + eps).computeCDF(point) - Triangular(distribution.getA(), distribution.getM(), distribution.getB() - eps).computeCDF(point)) / (2.0 * eps) print("cdf gradient (FD)=", repr(CDFgrFD)) # quantile quantile = distribution.computeQuantile(0.25) print("quantile=", repr(quantile)) print("cdf(quantile)=%.6f" % distribution.computeCDF(quantile)) # Define a point, right part of the support point = NumericalPoint(distribution.getDimension(), 2.0) print("Point= ", repr(point)) # 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[0] = (Triangular(distribution.getA() + eps, distribution.getM(), distribution.getB()).computePDF(point) - Triangular(distribution.getA() - eps, distribution.getM(), distribution.getB()).computePDF(point)) / (2.0 * eps) PDFgrFD[1] = (Triangular(distribution.getA(), distribution.getM() + eps, distribution.getB()).computePDF(point) - Triangular(distribution.getA(), distribution.getM() - eps, distribution.getB()).computePDF(point)) / (2.0 * eps) PDFgrFD[2] = (Triangular(distribution.getA(), distribution.getM(), distribution.getB() + eps).computePDF(point) - Triangular(distribution.getA(), distribution.getM(), distribution.getB() - 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] = (Triangular(distribution.getA() + eps, distribution.getM(), distribution.getB()).computeCDF(point) - Triangular(distribution.getA() - eps, distribution.getM(), distribution.getB()).computeCDF(point)) / (2.0 * eps) CDFgrFD[1] = (Triangular(distribution.getA(), distribution.getM() + eps, distribution.getB()).computeCDF(point) - Triangular(distribution.getA(), distribution.getM() - eps, distribution.getB()).computeCDF(point)) / (2.0 * eps) CDFgrFD[2] = (Triangular(distribution.getA(), distribution.getM(), distribution.getB() + eps).computeCDF(point) - Triangular(distribution.getA(), distribution.getM(), distribution.getB() - 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)) except: import sys print("t_Triangular_std.py", sys.exc_info()[0], sys.exc_info()[1])