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From "Zev Hochberg (JIRA)" <j...@apache.org>
Subject [jira] [Created] (MATH-888) GammaDistribution returns infinite density when cdf = 1
Date Tue, 30 Oct 2012 17:10:11 GMT
Zev Hochberg created MATH-888:
---------------------------------

             Summary: GammaDistribution returns infinite density when cdf = 1
                 Key: MATH-888
                 URL: https://issues.apache.org/jira/browse/MATH-888
             Project: Commons Math
          Issue Type: Bug
    Affects Versions: 3.0
         Environment: Windows 7
            Reporter: Zev Hochberg


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);            
        }
        System.out.println();
        
        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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