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.

Since:

1.4

See Also:

• Weron, R (1996). Statistics & Probability Letters. 28 (2): 165–171.

Nested Class Summary

Nested classes/interfaces inherited from class StableSampler

StableSampler.Alpha1CMSStableSampler, StableSampler.Beta0CMSStableSampler, StableSampler.Beta0WeronStableSampler, StableSampler.CMSStableSampler, StableSampler.SpecialMath, StableSampler.WeronStableSampler

Field Summary

Fields

Modifier and Type	Field	Description
protected final double	atanZeta	Cache of expression value used in generation.
protected final double	eps	Epsilon (1 - alpha).
protected final double	epsDiv1mEps	(1 / alpha) - 1 = eps / (1 - eps).
protected final double	inv1mEps	1 / alpha = 1 / (1 - eps).
protected final double	lower	The inclusive lower support for the distribution.
protected final double	meps1	Alpha (1 - eps).
protected final double	scale	Cache of expression value used in generation.
protected final double	upper	The inclusive upper support for the distribution.
protected final double	zeta	Cache of expression value used in generation.

Constructor Summary

Constructors

Constructor	Description
WeronStableSampler(UniformRandomProvider rng, double alpha, double beta)
WeronStableSampler(UniformRandomProvider rng, StableSampler.WeronStableSampler source)

Method Summary

Modifier and Type	Method	Description
protected double	createSample(double phi, double w)	Create the sample.
double	sample()	Generate a sample from a stable distribution.
StableSampler.WeronStableSampler	withUniformRandomProvider(UniformRandomProvider rng)	Create a new instance of the sampler with the same underlying state using the given uniform random provider as the source of randomness.

Methods inherited from class StableSampler.BaseStableSampler

getOmega, getPhi, getPhiBy2

Methods inherited from class StableSampler

nextLong, of, of, toString

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface ContinuousSampler

samples, samples

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