Alex Herbert created RNG-147:
--------------------------------
Summary: 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
[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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