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https://issues.apache.org/jira/browse/RNG-52?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16625654#comment-16625654
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Alex D Herbert commented on RNG-52:
-----------------------------------
OK. I'll add it to my TODO list for this week.
> PoissonSampler allows mean above Integer.MAX_VALUE
> --------------------------------------------------
>
> Key: RNG-52
> URL: https://issues.apache.org/jira/browse/RNG-52
> Project: Commons RNG
> Issue Type: Bug
> Components: sampling
> Affects Versions: 1.1
> Reporter: Alex D Herbert
> Priority: Major
> Fix For: 1.2
>
>
> The {{PoissonSampler}} is limited to returning an integer by the interface of
> the {{DiscreteSampler}}. As it stands an input mean above
> {{Integer.MAX_VALUE}} is allowed although it makes no sense as the Poisson
> distribution is significantly truncated.
> The algorithm of the {{SmallMeanPoissonSampler}} sets a limit on the returned
> sample of {{Integer.MAX_VALUE}}. The algorithm is valid although run-time
> would be impractical due to the nature of the algorithm. However at high mean
> (>40) the end user is expected to use either the {{LargeMeanPoissonSampler}}
> directly or the {{PoissonSampler}} which chooses the appropriate large mean
> algorithm.
> However the current {{LargeMeanPoissonSampler}} uses
> {{(int)Math.floor(mean)}} during initialisation and any mean above
> {{Integer.MAX_VALUE}} would therefore be unsupported.
> I propose to add this to the constructor of each Poisson sampler:
> {code:java}
> if (mean > Integer.MAX_VALUE) {
> throw new IllegalArgumentException(mean + " > " + Integer.MAX_VALUE);
> }
> {code}
> with documentation
> {code:java}
> * @throws IllegalArgumentException if {@code mean <= 0} or {@code mean >
> }{@link Integer.MAX_VALUE}.
> {code}
> It is noted that the limit of {{Integer.MAX_VALUE}} would allow the samples
> to reflect the Poisson distribution below that level but truncate it above
> that level to represent the remaining cumulative histogram at the single
> point of {{Integer.MAX_VALUE}}. This maintains the functionality of the
> sampler within the contract of the integer value returned by
> {{DiscreteSampler}}.
> In practice the Poisson distribution is unlikely to be used at such a high
> mean; in this case it is appropriate to use a Gaussian approximation to the
> Poisson.
> Note: Currently there is no code coverage from tests for the
> \{{LargeMeanPoissonSampler}} checking if the mean is <= 0. Tests should be
> added to check the constructor does throw when a bad mean is used.
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