[RNG-96] AhrensDieterMarsagliaTsangGammaSampler incorrectly names parameters

• Type: Bug
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 1.3
• Fix Version/s: 1.3
• Component/s: sampling
• Assignee: Alex Herbert
• Reporter: Alex Herbert
• Created: 24/Apr/19 16:14
• Updated: 12/Apr/20 11:19
• Resolved: 24/May/19 12:25

Description

The AhrensDieterMarsagliaTsangGammaSampler has parameters alpha and theta.

Using the naming conventions on Wikipedia Gamma distribution the alpha parameter is also known as the shape and the theta parameter is the scale:

// Wikipedia
alpha = shape
theta = scale

However if the sampler is run with the same parameters as the Wikipedia article histograms of the output sample distribution does not match. They need to be swapped indicating a naming mismatch.

Studying the same algorithm in o.a.c.math3.distribution.GammaDistribution it appears that the theta parameter is being used by Commons RNG as the shape and the alpha parameter is being used as the scale. So the names are incorrect and have been swapped.

// Commons RNG
alpha = scale (wrong)
theta = shape (wrong)

The unit tests for this sampler does this:

// Gamma (theta < 1).
add(LIST, new org.apache.commons.math3.distribution.GammaDistribution(unusedRng,

    thetaGammaSmallerThanOne, alphaGamma),

    new AhrensDieterMarsagliaTsangGammaSampler(
            RandomSource.create(RandomSource.XOR_SHIFT_1024_S),

            alphaGamma, thetaGammaSmallerThanOne));

// Gamma (theta > 1).
add(LIST, new org.apache.commons.math3.distribution.GammaDistribution(unusedRng, 

    thetaGammaLargerThanOne, alphaGamma),

    new AhrensDieterMarsagliaTsangGammaSampler(
              RandomSource.create(RandomSource.WELL_44497_B),
                                               
              alphaGamma, thetaGammaLargerThanOne));

This is a different parameter order for the two samplers.
So the tests enforce the fact that the parameters are swapped between Commons Math3 and Commons RNG.

Changing the actual parameter order would be a change of functionality. So this can be fixed by updating the Javadoc and parameter names for the sampler.

// Commons RNG
alpha renamed to theta (scale)
theta renamed to alpha (shape)

Issue Links

• causes: STATISTICS-23 Parameter names in "GammaDistribution"
• relates to: MATH-1373 In LogNormalDistribution.java, it appears shape & scale are reversed/mis-labelled.
• links to: GitHub Pull Request #39