com.numericalmethod.suanshu.stats.random.multivariate

Class NormalRvg

java.lang.Object

com.numericalmethod.suanshu.stats.random.multivariate.NormalRvg

All Implemented Interfaces:

RandomVectorGenerator, java.io.Serializable

public class NormalRvg
extends java.lang.Object
implements RandomVectorGenerator

A multivariate Normal random vector is said to be p-variate normally distributed if every linear combination of its p components has a univariate normal distribution. This implementation uses the "Best Approximation of Indefinite Matrices" in the reference. In the case where the covariance matrix is not positive definite, we force the diagonal elements in the eigen decomposition to a small non-negative number, e.g., 0. Then, we re-construct a positive definite matrix from the new diagonal elements.

The R equivalent function is rmvnorm in package mvtnorm.

See Also:

• Wikipedia: Multivariate normal distribution
• "Jin Wang, Chunlei Liu. "Generating Multivariate Mixture of Normal Distributions using a Modified Cholesky Decomposition," Simulation Conference, 2006. WSC 06. Proceedings of the Winter. p. 342 - 347. 3-6 Dec. 2006."

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
NormalRvg(int dim) Construct a standard multivariate Normal random vector generator.
NormalRvg(Vector mu, Matrix sigma) Construct a multivariate Normal random vector generator.
NormalRvg(Vector mu, Matrix sigma, RandomLongGenerator uniform, double epsilon) Construct a multivariate Normal random vector generator.

Method Summary

Modifier and Type	Method and Description
double[]	nextVector() Get the next random vector.
void	seed(long... seeds) Seed the random vector 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

NormalRvg

public NormalRvg(Vector mu,
                 Matrix sigma,
                 RandomLongGenerator uniform,
                 double epsilon)

Construct a multivariate Normal random vector generator.

Parameters:

mu - the mean

sigma - the covariance matrix

uniform - a uniform random number generator

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

NormalRvg

public NormalRvg(Vector mu,
                 Matrix sigma)

Construct a multivariate Normal random vector generator.

Parameters:

mu - the mean

sigma - the covariance matrix

NormalRvg

public NormalRvg(int dim)

Construct a standard multivariate Normal random vector generator.

Parameters:

dim - the dimension

Method Detail

seed

public void seed(long... seeds)

Description copied from interface: RandomVectorGenerator

Seed the random vector generator to produce repeatable sequences.

Specified by:

seed in interface RandomVectorGenerator

Parameters:

seeds - the seeds

nextVector

public double[] nextVector()

Description copied from interface: RandomVectorGenerator

Get the next random vector.

Specified by:

nextVector in interface RandomVectorGenerator

Returns:

the next random vector