[STATISTICS-39] Correct the switch of function evaluation in the GammaDistribution

• Type: Improvement
• Status: Closed
• Priority: Major
• Resolution: Fixed
• Affects Version/s: 1.0
• Fix Version/s: 1.0
• Component/s: distribution
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 07/Oct/21 18:26
• Updated: 06/Dec/22 11:30
• Resolved: 14/Dec/21 08:52

Description

The Gamma distribution density is not accurate when shape < 1. There are extensive tests related to MATH-753 [7] for accuracy of the Gamma distribution. These test shape >= 1. The work requires extension to smaller shapes where the density -> infinite as X -> 0. When shape >= 1 then density -> 0 as X -> 0 (see https://en.wikipedia.org/wiki/Gamma_distribution).

This results in inaccuracy of the Chi-squared distribution which uses Gamma(df/2, 2) when the degrees of freedom (df) are < 2. I've read the code and the documentation for the Boost functions which the code is based on and I think the switch to the alternative computation to avoid overflow is currently not working for all cases.

Issue Links

• relates to: NUMBERS-174 Update Gamma functions using the Boost implementation