PascalDistribution returns wrong values of mean and variance
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Key: MATH-715
URL: https://issues.apache.org/jira/browse/MATH-715
Project: Commons Math
Issue Type: Bug
Reporter: Sébastien Brisard
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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