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  1. Commons Math
  2. MATH-888

GammaDistribution returns infinite density when cdf = 1



    • Bug
    • Status: Closed
    • Major
    • Resolution: Fixed
    • 3.0
    • 3.1
    • None
    • None
    • Windows 7


      When GammaDistribution.cumulativeProbability = 1, then GammaDistribution.density may return Infinite - but it should return 0.
      Here is sample java code which demonstrates this issue, with results. Note that when pass the point at which cumulativeProbability = 1, the density stays > 0, though very small (pdf should be 0 when cdf = 1) - but as continue, then cdf stays 1, but pdf becomes infinite. This is seen most clearly in the second set of data below.

      package ApacheTester;

      import org.apache.commons.math3.distribution.GammaDistribution;

      public class GammaDistributionTester
      public static void main(String[] args)
      double mean = 10.118627813856065;
      double std = 0.8934747186204953;
      double alpha = (mean*mean)/(std*std);
      double beta = (std*std)/mean;
      System.out.println("alpha: " + alpha);
      System.out.println("beta: " + beta);

      GammaDistribution gd = new GammaDistribution(alpha, beta);

      for (int i=0; i<25; i++)

      { double pdf = gd.density(i); double cdf = gd.cumulativeProbability(i); System.out.println("i=" + i + "; pdf=" + pdf + "; cdf=" + cdf); }


      for (int i=0; i<20; i++)

      { double x = 19.0 + (.1 * i); double pdf = gd.density(x); double cdf = gd.cumulativeProbability(x); System.out.println("x=" + x + "; pdf=" + pdf + "; cdf=" + cdf); }


      Here's results of running above test:

      alpha: 128.25629996917283
      beta: 0.07889380729280462
      i=0; pdf=0.0; cdf=0.0
      i=1; pdf=8.663477060371509E-79; cdf=7.488555717749243E-81
      i=2; pdf=5.5062704634862175E-46; cdf=1.0676382015037016E-47
      i=3; pdf=4.413483488439264E-29; cdf=1.4607150065658644E-30
      i=4; pdf=1.0945225959157887E-18; cdf=5.599255664602861E-20
      i=5; pdf=7.35929647596093E-12; cdf=5.590805261026197E-13
      i=6; pdf=2.7437881760964153E-7; cdf=3.0732983691238435E-8
      i=7; pdf=2.8376132639470645E-4; cdf=4.7826733420766874E-5
      i=8; pdf=0.021281179160656388; cdf=0.005695853765034336
      i=9; pdf=0.2151187723352627; cdf=0.10175065472250033
      i=10; pdf=0.44751658755472723; cdf=0.4586536845007119
      i=11; pdf=0.259114059558244; cdf=0.8385256983930766
      i=12; pdf=0.05218255030958943; cdf=0.9781383380332821
      i=13; pdf=0.004329365023697574; cdf=0.9986058018679428
      i=14; pdf=1.6878342979402664E-4; cdf=0.9999549514385939
      i=15; pdf=3.431947471368873E-6; cdf=0.9999992047520807
      i=16; pdf=3.9588967227014906E-8; cdf=0.9999999917873332
      i=17; pdf=2.7752325350928474E-10; cdf=0.9999999999473412
      i=18; pdf=1.2515801802459923E-12; cdf=0.9999999999997794
      i=19; pdf=3.808710263354571E-15; cdf=0.9999999999999993
      i=20; pdf=8.143130333262255E-18; cdf=1.0
      i=21; pdf=Infinity; cdf=1.0
      i=22; pdf=Infinity; cdf=1.0
      i=23; pdf=Infinity; cdf=1.0
      i=24; pdf=Infinity; cdf=1.0

      x=19.0; pdf=3.808710263354571E-15; cdf=0.9999999999999993
      x=19.1; pdf=2.0912827149653448E-15; cdf=0.9999999999999997
      x=19.2; pdf=1.144280754920214E-15; cdf=0.9999999999999998
      x=19.3; pdf=6.239549206021272E-16; cdf=0.9999999999999999
      x=19.4; pdf=3.3907057624200243E-16; cdf=1.0
      x=19.5; pdf=1.8363629496980252E-16; cdf=1.0
      x=19.6; pdf=9.912278358035803E-17; cdf=1.0
      x=19.7; pdf=5.332732516340122E-17; cdf=1.0
      x=19.8; pdf=2.8595785047900534E-17; cdf=1.0
      x=19.9; pdf=1.5284263208928833E-17; cdf=1.0
      x=20.0; pdf=8.143130333262255E-18; cdf=1.0
      x=20.1; pdf=4.324705899342647E-18; cdf=1.0
      x=20.2; pdf=2.2895693394216285E-18; cdf=1.0
      x=20.3; pdf=1.2083606178165914E-18; cdf=1.0
      x=20.4; pdf=6.357672846520565E-19; cdf=1.0
      x=20.5; pdf=Infinity; cdf=1.0
      x=20.6; pdf=Infinity; cdf=1.0
      x=20.7; pdf=Infinity; cdf=1.0
      x=20.8; pdf=Infinity; cdf=1.0
      x=20.9; pdf=Infinity; cdf=1.0


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              zhochberg Zev Hochberg
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