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https://issues.apache.org/jira/browse/NUMBERS-174?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17449039#comment-17449039
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Alex Herbert commented on NUMBERS-174:
--------------------------------------
New code for review in [PR
110|https://github.com/apache/commons-numbers/pull/110]
Note: Currently the Travis CI integration with Github is not working for PRs.
Travis will build master but does not pick up PRs. So this should be verified
locally.
I tried changing .travis.yml to update the JDK environment from openjdk9 to
openjdk11 but this was not the cause since the master branch builds but not the
PR branch. No other changes to the .travis.yml have been done since the last PR
build 1 month ago ([Travis Commons Numbers
PRs|https://app.travis-ci.com/github/apache/commons-numbers/pull_requests]).
> Update Gamma functions using the Boost implementation
> -----------------------------------------------------
>
> Key: NUMBERS-174
> URL: https://issues.apache.org/jira/browse/NUMBERS-174
> Project: Commons Numbers
> Issue Type: Improvement
> Components: gamma
> Affects Versions: 1.0
> Reporter: Alex Herbert
> Assignee: Alex Herbert
> Priority: Major
> Fix For: 1.1
>
>
> The current regularised incomplete gamma functions for P and Q compute using
> a series representation for all input. This method is not robust to extreme
> arguments.
> The Gamma functions are used in Commons Statistics in the Gamma and Poisson
> distributions.
> Large values of the mean in the Poisson distribution have low
> precision for the CDF. The distribution also has a configurable
> threshold for convergence of the gamma function evaluation
> (STATISTICS-38). Ideally this implementation detail should be
> removed from the API.
> The Gamma distribution has a function switch based on a threshold to
> compute the PDF. This threshold results in incorrect values for
> certain parameters (STATISTICS-39).
> The function switch in the Gamma distribution is based on the
> documentation for the Boost gamma functions [1]. However it does not
> implement all the suggested optimisations detailed in the most recent
> Boost documentation. This includes avoiding using the converging
> series of the gamma function when the convergence is slow or unstable,
> i.e. addresses the need for a configurable convergence threshold in
> the Poisson distribution.
> One part of the evaluation of the incomplete gamma functions require
> accuracy in the leading term:
> {noformat}
> x^a exp(-x) / gamma(a) = exp(a log(x) - x - loggamma(a){noformat}
> When x and a are large then using logs to compute this leads to
> cancellation. Use of logs to compute this term is done in the current
> implementation in numbers for RegularizedGamma P and Q. It is the
> source of low precision for the CDF for the Poisson distribution when
> the mean is large.
> I propose to port the Boost gamma functions to numbers. This will be a
> process similar to the recent port of the error functions to the same
> package in numbers. These functions improved both accuracy and
> speed over the existing implementation. Once the gamma functions are
> ported a comparison can be made between the existing and new
> implementations.
> [1]
> [https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html]
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