Class StableSampler.CMSStableSampler

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

org.apache.commons.rng.sampling.distribution.StableSampler.CMSStableSampler

All Implemented Interfaces:

ContinuousSampler, SharedStateContinuousSampler, SharedStateSampler<SharedStateContinuousSampler>

Enclosing class:

StableSampler

static class StableSampler.CMSStableSampler
extends StableSampler.WeronStableSampler

Implement the generic stable distribution case: alpha < 2 and beta != 0. This routine assumes alpha != 1.

Implements the Chambers-Mallows-Stuck (CMS) method from Chambers, et al (1976) A Method for Simulating Stable Random Variables. Journal of the American Statistical Association Vol. 71, No. 354, pp. 340-344.

The formula produces a stable deviate from the 0-parameterization that is continuous at alpha=1.

This is an implementation of the Fortran routine RSTAB. In the event the computation fails then an alternative computation is performed 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. The error correction path is extremely unlikely to occur during use unless alpha -> 0. In general use it requires the random deviates w or u are extreme. See the unit tests for conditions that create them.

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

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
private static final double	HALF	1/2.
private final double	tau	Cache of expression value used in generation.

Fields inherited from class StableSampler.WeronStableSampler

atanZeta, eps, epsDiv1mEps, inv1mEps, lower, meps1, scale, upper, zeta

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
(package private) static double	getTau(double alpha, double beta)	Gets tau.
double	sample()	Generate a sample from a stable distribution.
StableSampler.CMSStableSampler	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.WeronStableSampler

createSample

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

HALF

private static final double HALF

1/2.

See Also:

• Constant Field Values

tau

private final double tau

Cache of expression value used in generation.

Constructor Details

CMSStableSampler

CMSStableSampler(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].

CMSStableSampler

CMSStableSampler(UniformRandomProvider rng,
 StableSampler.CMSStableSampler source)

Parameters:

rng - Underlying source of randomness

source - Source to copy.

Method Details

getTau

static double getTau(double alpha,
 double beta)

Gets tau. This is a factor used in the CMS algorithm. If this is zero then a special case of beta -> 0 has occurred.

Parameters:

alpha - Stability parameter. Must be in the interval (0, 2].

beta - Skewness parameter. Must be in the interval [-1, 1].

Returns:

tau

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

Overrides:

sample in class StableSampler.WeronStableSampler

Returns:

a sample.

withUniformRandomProvider

public StableSampler.CMSStableSampler 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>

Overrides:

withUniformRandomProvider in class StableSampler.WeronStableSampler

Parameters:

rng - Generator of uniformly distributed random numbers.

Returns:

the sampler