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https://issues.apache.org/jira/browse/RNG-147?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Alex Herbert resolved RNG-147.
------------------------------
Fix Version/s: 1.4
Resolution: Implemented
> LevySampler
> -----------
>
> Key: RNG-147
> URL: https://issues.apache.org/jira/browse/RNG-147
> Project: Commons RNG
> Issue Type: New Feature
> Components: sampling
> Affects Versions: 1.3
> Reporter: Alex Herbert
> Priority: Minor
> Fix For: 1.4
>
>
> [Sampling from a Levy
> distribution|https://en.wikipedia.org/wiki/L%C3%A9vy_distribution#Random_sample_generation]
> is done using an inverse transform of the cumulative distribution function
> of the standard normal distribution.
> {noformat}
> Levy(Z) = 1
> -------------------
> (inv CDF_norm(u))^2
> {noformat}
> With u a uniform deviate in [0, 1). An alternative is direct generation of a
> uniform normal variate with mean 0 and standard deviation 1: N(0, 1):
> {noformat}
> Levy(Z) = 1
> --------
> N(0,1)^2
> {noformat}
> This should be faster than inverse transform sampling if generation of the
> normal distribution sample is faster than computation of the inverse
> cumulative probability function.
> This sampler can be used in Commons Statistics for the Levy distribution.
> The extremes of the support should be investigated, i.e. what is the maximum
> value for a sample from a standard normal distribution such as the
> ZigguratNormalizedGaussianSampler vs the maximum value of the inverse CDF of
> the normal distribution when the uniform deviate is at the upper limit of 1 -
> 2^-53.
>
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