Package org.apache.commons.rng.sampling.distribution

Class StableSampler.WeronStableSampler

java.lang.Object
org.apache.commons.rng.sampling.distribution.StableSampler
org.apache.commons.rng.sampling.distribution.StableSampler.BaseStableSampler
org.apache.commons.rng.sampling.distribution.StableSampler.WeronStableSampler
All Implemented Interfaces:
ContinuousSampler, SharedStateContinuousSampler, SharedStateSampler<SharedStateContinuousSampler>
Direct Known Subclasses:
StableSampler.CMSStableSampler
Enclosing class:
StableSampler
static class StableSampler.WeronStableSampler extends StableSampler.BaseStableSampler
Implement the generic stable distribution case: alpha < 2 and beta != 0. This routine assumes alpha != 1.

Implements the Chambers-Mallows-Stuck (CMS) method using the formula provided in Weron (1996) "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables" Statistics & Probability Letters. 28 (2): 165–171. This method is easier to correct from infinite and NaN results by boxing intermediate infinite values.

The formula produces a stable deviate from the 1-parameterization that is discontinuous at alpha=1. A shift is used to create the 0-parameterization. This shift is very large as alpha -> 1 and the output loses bits of precision in the deviate due to cancellation. It is not recommended to use this sampler when alpha -> 1 except for edge case correction.

This produces non-NaN output for all parameters alpha, beta, u and w with the correct orientation for extremes of the distribution support. The formulas used are symmetric with regard to beta and u.

See Also:

  • Field Details

    • eps

      protected final double eps
      Epsilon (1 - alpha).

    • meps1

      protected final double meps1
      Alpha (1 - eps).

    • zeta

      protected final double zeta
      Cache of expression value used in generation.

    • atanZeta

      protected final double atanZeta
      Cache of expression value used in generation.

    • scale

      protected final double scale
      Cache of expression value used in generation.

    • inv1mEps

      protected final double inv1mEps
      1 / alpha = 1 / (1 - eps).

    • epsDiv1mEps

      protected final double epsDiv1mEps
      (1 / alpha) - 1 = eps / (1 - eps).

    • lower

      protected final double lower
      The inclusive lower support for the distribution.

    • upper

      protected final double upper
      The inclusive upper support for the distribution.

  • Constructor Details

    • WeronStableSampler

      WeronStableSampler(UniformRandomProvider rng, double alpha, double beta)
      Parameters:
      rng - Underlying source of randomness
      alpha - Stability parameter. Must be in the interval (0, 2].
      beta - Skewness parameter. Must be in the interval [-1, 1].

    • WeronStableSampler

      WeronStableSampler(UniformRandomProvider rng, StableSampler.WeronStableSampler source)
      Parameters:
      rng - Underlying source of randomness
      source - Source to copy.

  • Method Details

    • sample

      public double sample()
      Description copied from class: StableSampler
      Generate a sample from a stable distribution.

      The distribution uses the 0-parameterization: S(alpha, beta, gamma, delta; 0).

      Specified by:
      sample in interface ContinuousSampler
      Specified by:
      sample in class StableSampler
      Returns:
      a sample.

    • createSample

      protected double createSample(double phi, double w)
      Create the sample. This routine is robust to edge cases and returns a deviate at the extremes of the support. It correctly handles alpha -> 0 when the sample is increasingly likely to be +/- infinity.
      Parameters:
      phi - Uniform deviate in (-pi/2, pi/2)
      w - Exponential deviate
      Returns:
      x

    • withUniformRandomProvider

      public StableSampler.WeronStableSampler withUniformRandomProvider(UniformRandomProvider rng)
      Description copied from class: StableSampler
      Create a new instance of the sampler with the same underlying state using the given uniform random provider as the source of randomness.
      Specified by:
      withUniformRandomProvider in interface SharedStateSampler<SharedStateContinuousSampler>
      Specified by:
      withUniformRandomProvider in class StableSampler
      Parameters:
      rng - Generator of uniformly distributed random numbers.
      Returns:
      the sampler