Class StableSampler.WeronStableSampler
- All Implemented Interfaces:
ContinuousSampler
,SharedStateContinuousSampler
,SharedStateSampler<SharedStateContinuousSampler>
- Direct Known Subclasses:
StableSampler.CMSStableSampler
- Enclosing class:
StableSampler
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:
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Nested Class Summary
Nested classes/interfaces inherited from class org.apache.commons.rng.sampling.distribution.StableSampler
StableSampler.Alpha1CMSStableSampler, StableSampler.Beta0CMSStableSampler, StableSampler.Beta0WeronStableSampler, StableSampler.CMSStableSampler, StableSampler.SpecialMath, StableSampler.WeronStableSampler
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected final double
Cache of expression value used in generation.protected final double
Epsilon (1 - alpha).protected final double
(1 / alpha) - 1 = eps / (1 - eps).protected final double
1 / alpha = 1 / (1 - eps).protected final double
The inclusive lower support for the distribution.protected final double
Alpha (1 - eps).protected final double
Cache of expression value used in generation.protected final double
The inclusive upper support for the distribution.protected final double
Cache of expression value used in generation. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionprotected double
createSample
(double phi, double w) Create the sample.double
sample()
Generate a sample from a stable distribution.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 org.apache.commons.rng.sampling.distribution.StableSampler.BaseStableSampler
getOmega, getPhi, getPhiBy2
Methods inherited from class org.apache.commons.rng.sampling.distribution.StableSampler
nextLong, of, of, toString
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
Methods inherited from interface org.apache.commons.rng.sampling.distribution.ContinuousSampler
samples, samples
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Field Details
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eps
protected final double epsEpsilon (1 - alpha). -
meps1
protected final double meps1Alpha (1 - eps). -
zeta
protected final double zetaCache of expression value used in generation. -
atanZeta
protected final double atanZetaCache of expression value used in generation. -
scale
protected final double scaleCache of expression value used in generation. -
inv1mEps
protected final double inv1mEps1 / alpha = 1 / (1 - eps). -
epsDiv1mEps
protected final double epsDiv1mEps(1 / alpha) - 1 = eps / (1 - eps). -
lower
protected final double lowerThe inclusive lower support for the distribution. -
upper
protected final double upperThe inclusive upper support for the distribution.
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Constructor Details
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WeronStableSampler
WeronStableSampler(UniformRandomProvider rng, double alpha, double beta) - Parameters:
rng
- Underlying source of randomnessalpha
- Stability parameter. Must be in the interval(0, 2]
.beta
- Skewness parameter. Must be in the interval[-1, 1]
.
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WeronStableSampler
WeronStableSampler(UniformRandomProvider rng, StableSampler.WeronStableSampler source) - Parameters:
rng
- Underlying source of randomnesssource
- Source to copy.
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Method Details
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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 interfaceContinuousSampler
- Specified by:
sample
in classStableSampler
- Returns:
- a sample.
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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 handlesalpha -> 0
when the sample is increasingly likely to be +/- infinity.- Parameters:
phi
- Uniform deviate in(-pi/2, pi/2)
w
- Exponential deviate- Returns:
- x
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withUniformRandomProvider
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 interfaceSharedStateSampler<SharedStateContinuousSampler>
- Specified by:
withUniformRandomProvider
in classStableSampler
- Parameters:
rng
- Generator of uniformly distributed random numbers.- Returns:
- the sampler
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