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https://issues.apache.org/jira/browse/MATH-753?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Sébastien Brisard updated MATH-753:
-----------------------------------
Attachment: lanczos.patch
{{lanczos.patch}} is the patch discussed in the the {{dev}} mailing-list:
{quote}
As I initially feared, what was proposed in the JIRA ticket leads to high
floating point errors. I adapted a method proposed in
[BOOST|http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html]
(formula (15))
with acceptable errors. Meanwhile, I've also managed to improve the accuracy of
the computation of the density for the range of parameters where the previous
implementation was already working: in this range, the accuracy _was_ about 300
ulps, and is now 1-2 ulps! {color:red}Note: I might have been too optimistic,
here. There is a significant improvement, though{color}. I think this
improvement is worth implementing.
The downside is that I need to expose the Lanczos implementation internally
used by {{o.a.c.m3.special.Gamma}}. This approximation is so standard that I
don't see it as a problem. I don't think that it reveals too much of the Gamma
internals, since the javadoc of {{Gamma.logGamma}} states that it uses this
approximation. So what I
propose is the addition of two methods in {{Gamma}}:
* {{double getLanczosG()}}: returns the {{g}} constant
* {{double lanczos(double)}}: returns the value of the Lanczos sum.
{quote}
> Better implementation for the gamma distribution density function
> -----------------------------------------------------------------
>
> Key: MATH-753
> URL: https://issues.apache.org/jira/browse/MATH-753
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 2.2, 3.0, 3.1
> Reporter: Francesco Strino
> Assignee: Sébastien Brisard
> Priority: Minor
> Labels: improvement, stability
> Fix For: 3.1
>
> Attachments: lanczos.patch
>
>
> The way the density of the gamma distribution function is estimated can be
> improved.
> It's much more stable to calculate first the log of the density and then
> exponentiate, otherwise the function returns NaN for high values of the
> parameters alpha and beta.
> It would be sufficient to change the public double density(double x) function
> at line 204 in the file
> org.apache.commons.math.distribution.GammaDistributionImpl as follows:
> return Math.exp(Math.log( x )*(alpha-1) - Math.log(beta)*alpha - x/beta -
> Gamma.logGamma(alpha));
> In order to improve performance, log(beta) and Gamma.logGamma(alpha) could
> also be precomputed and stored during initialization.
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