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https://issues.apache.org/jira/browse/MATH-715?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Sébastien Brisard closed MATH-715.
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Fixed in 3.0.
> PascalDistribution returns wrong values of mean and variance
> ------------------------------------------------------------
>
> Key: MATH-715
> URL: https://issues.apache.org/jira/browse/MATH-715
> Project: Commons Math
> Issue Type: Bug
> Reporter: Sébastien Brisard
> Assignee: Sébastien Brisard
> Fix For: 3.0
>
>
> The header of the Javadoc states that the random variable (say X) being
> represented by this {{o.a.c.m.distribution.PascalDistribution}} is the number
> of *failures*. The current Javadoc is slightly confusing, because it refers
> to the Wikipedia website, where the opposite convention is adopted (X is the
> number of *successes*) : different formulas therefore apply for the mean and
> variance of X. The javadoc should be made clearer, for example by inclusion
> of full formulas. Also the parameters differing from the Wikipedia reference
> should not have the same name
> * {{p}} is the probability of success in both cases: OK,
> * {{r}} is the number of failures in Wikipedia, but the number of successes
> in CM. This could be renamed (say) {{s}}.
> Finally, with the current notations of CM, the mean of X is given by
> {{mean(X) = r * (1 - p) / p}}, while the currently implemented formula is {{r
> * p / (1 - p)}}, which is actually the formula corresponding to the Wikipedia
> convention.
> The following piece of code shows that the current implementation is faulty
> {code:java}
> public class PascalDistributionDemo {
> public static void main(String[] args) {
> final int r = 10;
> final double p = 0.2;
> final int numTerms = 1000;
> final PascalDistribution distribution = new PascalDistribution(r, p);
> double mean = 0.;
> for (int k = numTerms - 1; k >= 0; k--) {
> mean += k * distribution.probability(k);
> }
> // The following prints 40.00000000000012
> System.out.println("Estimate of the mean = " + mean);
> // The following prints 2.5
> System.out.println("CM implementation = " +
> distribution.getNumericalMean());
> // The following prints 2.5
> System.out.println("r * p / (1 - p) = " + (r * p / (1 - p)));
> // The following prints 40.0
> System.out.println("r * (1 - p) / p = " + (r * (1 - p) / p));
> }
> }
> {code}
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