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https://issues.apache.org/jira/browse/RNG-96?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16826082#comment-16826082
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Gilles commented on RNG-96:
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{quote}OK. So update the sampler so that the parameter order and meaning is the
same as Commons Math 3:
alpha = shape
theta = scale
{quote}
I'm lost now. The issue (confusing names) was initially reported against CM3.
I'd thought that the names {{shape}} and {{scale}} should disappear from the
docs.
{quote}IIUC that would be just be a parameter swap in the following method:
{quote}
As per the above, it would be clearer (IMHO) to only refer to names used on the
Wikipedia and MathWorld pages (i.e. α and θ).
{quote}add a Jira ticket to do this to Commons Statistics and link this?
{quote}
Sure. Thank you!
> AhrensDieterMarsagliaTsangGammaSampler incorrectly names parameters
> -------------------------------------------------------------------
>
> Key: RNG-96
> URL: https://issues.apache.org/jira/browse/RNG-96
> Project: Commons RNG
> Issue Type: Bug
> Components: sampling
> Affects Versions: 1.3
> Reporter: Alex D Herbert
> Assignee: Alex D Herbert
> Priority: Minor
> Fix For: 1.3
>
>
> The AhrensDieterMarsagliaTsangGammaSampler has parameters alpha and theta.
> Using the naming conventions on [Wikipedia Gamma
> distribution|https://en.wikipedia.org/wiki/Gamma_distribution] the alpha
> parameter is also known as the shape and the theta parameter is the scale:
> {noformat}
> // Wikipedia
> alpha = shape
> theta = scale
> {noformat}
> 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.
> {noformat}
> // Commons RNG
> alpha = scale (wrong)
> theta = shape (wrong)
> {noformat}
> The unit tests for this sampler does this:
> {code:java}
> // 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));
> {code}
> 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.
> {noformat}
> // Commons RNG
> alpha renamed to theta (scale)
> theta renamed to alpha (shape)
> {noformat}
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