[jira] [Resolved] (RNG-147) LevySampler

["Alex Herbert (Jira)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/RNG-147?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

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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