[jira] [Created] (STATISTICS-34) Geometric distribution to switch PMF computation for increased accuracy

["Alex Herbert (Jira)" <ji...@apache.org>]

Alex Herbert created STATISTICS-34:
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             Summary: Geometric distribution to switch PMF computation for increased accuracy
                 Key: STATISTICS-34
                 URL: https://issues.apache.org/jira/browse/STATISTICS-34
             Project: Apache Commons Statistics
          Issue Type: Improvement
          Components: distribution
    Affects Versions: 1.0
            Reporter: Alex Herbert
             Fix For: 1.0


The Geometric distribution is define by the probability of success (p).

The PMF is:
{noformat}
pmf(x) = pow(1 - p, x) * p
{noformat}

This can be implemented directly or using exponential functions:

{code:java}
double p1 = Math.pow(1.0 - p, x) * p;
double p2 = Math.exp(Math.log1p(-p) * x) * p;
{code}

The current code uses exponential functions. Implementations in Matlab, R and SciPy all use the power function. Both have advantages depending on the value of p.

When p is >= 0.5 the value (1-p) is exact. As p becomes increasingly small then (1-p) loses precision due to the limited precision of a double value close to 1.




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