com.numericalmethod.suanshu.stats.random.univariate

Class InverseTransformSampling

java.lang.Object

com.numericalmethod.suanshu.stats.random.univariate.InverseTransformSampling

All Implemented Interfaces:

RandomNumberGenerator, java.io.Serializable

Direct Known Subclasses:

InverseTransformSamplingExpRng, InverseTransformSamplingGammaRng, RayleighRng, WeibullRng

public class InverseTransformSampling
extends java.lang.Object
implements RandomNumberGenerator

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, golden rule, etc.) is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its cumulative distribution function. This basic idea is this: to generate a random variable X with a cumulative distribution function F(x) for all x, we first sample u from the uniform distribution. Then, x = F^-1(u) = Q(u). This method requires that F(x) has a continuous density function, hence, strictly increasing and its inverse well defined.

See Also:

• "Paul Glasserman. "p. 44," Monte Carlo Methods in Financial Engineering, 2004."
• Wikipedia: Inverse transform sampling

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
InverseTransformSampling(ProbabilityDistribution distribution) Construct a random number generator to sample from a distribution.
InverseTransformSampling(ProbabilityDistribution distribution, RandomLongGenerator uniform) Construct a random number generator to sample from a distribution.

Method Summary

Modifier and Type	Method and Description
double	nextDouble() Get the next random double.
void	seed(long... seeds) Seed the random number generator to produce repeatable sequences.

Methods inherited from class java.lang.Object

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

Constructor Detail

InverseTransformSampling

public InverseTransformSampling(ProbabilityDistribution distribution,
                                RandomLongGenerator uniform)

Construct a random number generator to sample from a distribution.

Parameters:

distribution - the distribution to sample from

uniform - a uniform random number generator that samples between 0 and 1

InverseTransformSampling

public InverseTransformSampling(ProbabilityDistribution distribution)

Construct a random number generator to sample from a distribution.

Parameters:

distribution - the distribution to sample from

Method Detail

seed

public void seed(long... seeds)

Description copied from interface: RandomNumberGenerator

Seed the random number generator to produce repeatable sequences.

Specified by:

seed in interface RandomNumberGenerator

Parameters:

seeds - the seeds

nextDouble

public double nextDouble()

Description copied from interface: RandomNumberGenerator

Get the next random double.

Specified by:

nextDouble in interface RandomNumberGenerator

Returns:

the next random number