Package umontreal.iro.lecuyer.randvar

This package provides a collection of classes for non-uniform random variate generation, primarily from standard distributions.

See:
Description

Class Summary

BernoulliGen	This class implements random variate generators for the Bernoulli distribution (see class BernoulliDist).
BetaGen	This class implements random variate generators with the beta distribution with shape parameters α > 0 and β > 0, over the interval (a, b), where a < b.
BetaRejectionLoglogisticGen	Implements Beta random variate generators using the rejection method with log-logistic envelopes.
BetaStratifiedRejectionGen	This class implements Beta random variate generators using the stratified rejection/patchwork rejection method.
BetaSymmetricalBestGen	This class implements symmetrical beta random variate generators using Devroye's one-liner method.
BetaSymmetricalGen	This class implements random variate generators with the symmetrical beta distribution with shape parameters α = β, over the interval (0, 1).
BetaSymmetricalPolarGen	This class implements symmetrical beta random variate generators using Ulrich's polar method.
BinomialConvolutionGen	Implements binomial random variate generators using the convolution method.
BinomialGen	This class implements random variate generators for the binomial distribution.
CauchyGen	This class implements random variate generators for the Cauchy distribution.
ChiGen	This class implements random variate generators for the chi distribution.
ChiRatioOfUniformsGen	This class implements Chi random variate generators using the ratio of uniforms method with shift.
ChiSquareGen	This class implements random variate generators with the chi square distribution with n > 0 degrees of freedom.
ChiSquareNoncentralGamGen	This class implements noncentral chi square random variate generators using the additive property of the noncentral chi square distribution.
ChiSquareNoncentralGen	This class implements random variate generators for the noncentral chi square distribution with ν > 0 degrees of freedom and noncentrality parameter λ > 0.
ChiSquareNoncentralPoisGen	This class implements noncentral chi square random variate generators using Poisson and central chi square generators.
ConstantGen	This class implements a random variate generator that returns a constant value.
ErlangConvolutionGen	This class implements Erlang random variate generators using the convolution method.
ErlangGen	This class implements random variate generators for the Erlang distribution with parameters k > 0 and λ > 0.
ExponentialGen	This class implements random variate generators for the exponential distribution.
ExponentialInverseFromDensityGen	This class implements exponential random variate generators using numerical inversion of the exponential density as described in.
ExtremeValueGen	Deprecated.
FatigueLifeGen	This class implements random variate generators for the fatigue life distribution with location parameter μ, scale parameter β and shape parameter γ.
FisherFGen	This class implements random variate generators for the Fisher F distribution with n and m degrees of freedom, where n and m are positive integers.
FNoncentralGen	This class implements random variate generators for the noncentral F-distribution.
FoldedNormalGen	This class implements methods for generating random variates from the folded normal distribution with parameters μ >= 0 and σ > 0.
FrechetGen	This class implements methods for generating random variates from the Fréchet distribution, with location parameter δ, scale parameter β > 0, and shape parameter α > 0, where we use the notation z = (x - δ)/β.
GammaAcceptanceRejectionGen	This class implements gamma random variate generators using a method that combines acceptance-rejection with acceptance-complement.
GammaGen	This class implements random variate generators for the gamma distribution.
GammaRejectionLoglogisticGen	This class implements gamma random variate generators using a rejection method with loglogistic envelopes,.
GeometricGen	This class implements a random variate generator for the geometric distribution.
GumbelGen	This class implements methods for generating random variates from the Gumbel distribution.
HalfNormalGen	This class implements methods for generating random variates from the half-normal distribution with parameters μ and σ > 0.
HyperbolicSecantGen	This class implements random variate generators for the hyperbolic secant distribution with location parameter μ and scale parameter σ.
HypergeometricGen	This class implements random variate generators for the hypergeometric distribution.
HypoExponentialGen	This class implements random variate generators for the hypoexponential distribution (see classes HypoExponentialDist and HypoExponentialDistQuick in package probdist for the definition).
InverseFromDensityGen	Implements a method for generating random variates by numerical inversion of an arbitrary continuous distribution when only the probability density is known.
InverseGammaGen	This class implements random variate generators for the inverse gamma distribution with shape parameter α > 0 and scale parameter β > 0.
InverseGaussianGen	This class implements random variate generators for the inverse Gaussian distribution with location parameter μ > 0 and scale parameter λ > 0.
InverseGaussianMSHGen	This class implements inverse gaussian random variate generators using the many-to-one transformation method of Michael, Schucany and Haas (MHS).
JohnsonSBGen	This class implements random variate generators for the Johnson SB distribution.
JohnsonSLGen	This class implements random variate generators for the Johnson SL distribution.
JohnsonSUGen	This class implements random variate generators for the Johnson SU distribution.
KernelDensityGen	This class implements random variate generators for distributions obtained via kernel density estimation methods from a set of n individual observations x1,..., xn.
KernelDensityVarCorrectGen	This class is a variant of KernelDensityGen, but with a rescaling of the empirical distribution so that the variance of the density used to generate the random variates is equal to the empirical variance, as suggested by Silverman.
LaplaceGen	This class implements methods for generating random variates from the Laplace distribution.
LogarithmicGen	This class implements random variate generators for the (discrete) logarithmic distribution.
LogisticGen	This class implements random variate generators for the logistic distribution.
LoglogisticGen	This class implements random variate generators for the log-logistic distribution with shape parameter α > 0 and scale parameter β > 0.
LognormalGen	This class implements methods for generating random variates from the lognormal distribution.
LognormalSpecialGen	Implements methods for generating random variates from the lognormal distribution using an arbitrary normal random variate generator.
NakagamiGen	This class implements random variate generators for the Nakagami distribution.
NegativeBinomialGen	This class implements random variate generators having the negative binomial distribution.
NormalACRGen	This class implements normal random variate generators using the acceptance-complement ratio method.
NormalBoxMullerGen	This class implements normal random variate generators using the Box-Muller method.
NormalGen	This class implements methods for generating random variates from the normal distribution N(μ, σ).
NormalInverseFromDensityGen	This class implements normal random variate generators using numerical inversion of the normal density as described in.
NormalInverseGaussianGen	This class implements random variate generators for the normal inverse gaussian (NIG) distribution.
NormalInverseGaussianIGGen	.
NormalKindermannRamageGen	This class implements normal random variate generators using the Kindermann-Ramage method.
NormalPolarGen	This class implements normal random variate generators using the polar method with rejection.
ParetoGen	This class implements random variate generators for one of the Pareto distributions, with parameters α > 0 and β > 0.
PascalConvolutionGen	Implements Pascal random variate generators by the convolution method.
PascalGen	Implements Pascal random variate generators, which is a special case of the negative binomial generator with parameter γ equal to a positive integer.
Pearson5Gen	Deprecated.
Pearson6Gen	This class implements random variate generators for the Pearson type VI distribution with shape parameters α1 > 0 and α2 > 0, and scale parameter β > 0.
PoissonGen	This class implements random variate generators having the Poisson distribution.
PoissonTIACGen	This class implements random variate generators having the Poisson distribution (see PoissonGen).
PowerGen	This class implements random variate generators for the power distribution with shape parameter c > 0, over the interval [a, b].
RandomVariateGen	This is the base class for all random variate generators over the real line.
RandomVariateGenInt	This is the base class for all generators of discrete random variates over the set of integers.
RandomVariateGenWithCache	This class represents a random variate generator whose values are cached for more efficiency when using common random numbers.
RayleighGen	This class implements random variate generators for the Rayleigh distribution.
StudentGen	This class implements methods for generating random variates from the Student distribution with n > 0 degrees of freedom.
StudentNoncentralGen	This class implements random variate generators for the noncentral Student-t distribution with n > 0 degrees of freedom and noncentrality parameter δ.
StudentPolarGen	This class implements Student random variate generators using the polar method of.
TriangularGen	This class implements random variate generators for the triangular distribution.
UniformGen	This class implements random variate generators for the (continuous) uniform distribution over the interval (a, b), where a and b are real numbers with a < b.
UniformIntGen	This class implements a random variate generator for the uniform distribution over integers, over the interval [i, j].
UnuranContinuous	This class permits one to create continuous univariate generators using UNURAN via its string API.
UnuranDiscreteInt	This class permits one to create a discrete univariate generator using UNURAN via its string API.
UnuranEmpirical	This class permits one to create generators for empirical and quasi-empirical univariate distributions using UNURAN via its string interface.
WeibullGen	This class implements random variate generators for the Weibull distribution.

Exception Summary

UnuranException

This type of unchecked exception is thrown when an error occurs inside the UNURAN package.

Package umontreal.iro.lecuyer.randvar Description

This package provides a collection of classes for non-uniform random variate generation, primarily from standard distributions.

Each non-uniform random variate generator requires at least one RandomStream object (from package rng), used to generate the underlying uniform random numbers.

The generic classes RandomVariateGen and RandomVariateGenInt permit one to construct a random variate generator from a random stream and an arbitrary distribution (see interface Distribution). To generate random variates by inversion from an arbitrary distribution over the real numbers using a given random stream, it suffices to construct a RandomVariateGen object with the desired (previously created) Distribution and RandomStream objects, and then call its nextDouble method as many times as needed. For discrete distributions over the integers, one can construct a RandomVariateGenInt object containing the desired DiscreteDistributionInt and RandomStream, and call its nextInt method. By default, these generators simply call the inverseF method from the specified distribution object. These two classes suffice as long as we are willing to use inversion. Here is a simple example in which we create three parallel streams of normal random variates using inversion.

[label=lst:normaltest,caption=Using three parallel streams of random normal variates,lineskip=-2pt,emph=genere,main ]exam/normaltest.java

To generate random variates by other methods than inversion, one can use specialized classes that extend RandomVariateGen or RandomVariateGenInt. Such classes are provided for a variety of standard discrete and continuous distributions. For example, five different subclasses implement normal random variate generators, using five different methods. One of them, the class NormalGen, extends RandomVariateGen directly and provides normal random variate generators based on inversion, so it does the same thing as using RandomVariateGen with the normal distribution. The others are subclasses of NormalGen; they implement various non-inversion normal variate generation methods. To generate random variates with a specific method, it suffices to construct an object of the appropriate subclass and then call its nextDouble method.

In most cases, the specialized classes maintain local copies of the distribution parameters and use them for variate generation. If the parameters of the contained distribution objects are later modified, this may lead to inconsistencies: the variate generator object will keep using the old values. In fact, the constructors of the specialized classes often precompute constants and tables based on these parameter values, which would have to be recomputed if the parameters are changed. On the other hand, the generic classes RandomVariateGen and RandomVariateGenInt call directly the inverseF method of the contained distribution object, so they will always use the new parameter values whenever the parameters in the distribution object are changed.

With some variate generation methods (e.g., the rejection method), the number of uniforms required to get a single non-uniform variate varies from one call to the next. In that case, an auxiliary stream is often used to preserve the synchronization between random variates when implementing variance-reduction methods. The main random number stream is called a fixed number of times per non-uniform variate generation. If more uniform random numbers are needed, they are obtained from the auxiliary stream. For these types of generators, two RandomStream objects should be passed to the constructor. Otherwise, by default, the same stream will be used for all uniforms.

Static methods in the specialized classes allow the generation of random variates from specific distributions without constructing a RandomVariateGen object.

This package also provides an interface to the UNURAN (Universal Non-Uniform RANdom number generators) package, a rich library of C functions designed and implemented by the ARVAG (Automatic Random VAriate Generation) project group in Vienna. This interface can be used to access distributions or generation methods not available directly in SSJ. To get a UNURAN generator, it suffices to instantiate one of the UNURAN interface classes: UnuranDiscreteInt for discrete random variates, UnuranContinuous for continuous ones (in one dimension), and UnuranEmpirical for quasi-empirical distributions based on experimental data. The type of distribution and its parameters are specified to UNURAN via its String API (see the UNURAN documentation). Only univariate distributions are supported because the UNURAN String API does not support the multivariate ones yet.

In the UNURAN interface classes, nextDouble and nextInt can be invoked as usual to generate variates, but these methods are slowed down significantly by the overhead in the interactions between code on the native side and on the Java side. When several random variates are needed, it is much more efficient to generate them in a single call, via the methods nextArrayOfDouble and nextArrayOfInt.