[STATISTICS-34] Geometric distribution to switch PMF computation for increased accuracy

• Type: Improvement
• Status: Closed
• Priority: Trivial
• Resolution: Fixed
• Affects Version/s: 1.0
• Fix Version/s: 1.0
• Component/s: distribution
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 21/Sep/21 15:03
• Updated: 06/Dec/22 11:30
• Resolved: 07/Oct/21 18:47

Description

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

The PMF is:

pmf(x) = pow(1 - p, x) * p

This can be implemented directly or using exponential functions:

double p1 = Math.pow(1.0 - p, x) * p;
double p2 = Math.exp(Math.log1p(-p) * x) * p;

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.