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https://issues.apache.org/jira/browse/RNG-96?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16826098#comment-16826098
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Alex D Herbert commented on RNG-96:
-----------------------------------
{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}
Wikipedia uses [shape|https://en.wikipedia.org/wiki/Shape_parameter]:
{noformat}
In probability theory and statistics, a shape parameter is a kind of numerical
parameter of a parametric family of probability distributions.[1]
Specifically, a shape parameter is any parameter of a probability distribution
that is neither a location parameter nor a scale parameter (nor a function of
either or both of these only, such as a rate parameter). Such a parameter must
affect the shape of a distribution rather than simply shifting it (as a
location parameter does) or stretching/shrinking it (as a scale parameter does).
{noformat}
and [scale|https://en.wikipedia.org/wiki/Scale_parameter]:
{noformat}
In probability theory and statistics, a scale parameter is a special kind of
numerical parameter of a parametric family of probability distributions. The
larger the scale parameter, the more spread out the distribution.
{noformat}
Given these definitions I think they are useful.
It could be made more explicit by changing the constructor to:
{code:java}
/**
* @param rng Generator of uniformly distributed random numbers.
* @param alpha Alpha parameter of the distribution (this is a shape parameter).
* @param theta Theta parameter of the distribution (this is a scale parameter).
* @throws IllegalArgumentException if {@code alpha <= 0} or {@code theta <= 0}
*/
public AhrensDieterMarsagliaTsangGammaSampler(UniformRandomProvider rng,
double alpha,
double theta) {
{code}
Thus a user converting from CM3 which uses shape and scale as the parameter
names will know this is equivalent.
> 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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