Package dev.nm.stat.random.rng.multivariate

Class NormalRVG

java.lang.Object

dev.nm.stat.random.rng.multivariate.NormalRVG

All Implemented Interfaces:

RandomVectorGenerator, Seedable

public class NormalRVG
extends 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."

Constructor Summary

Constructors

Constructor	Description
NormalRVG(int dim)	Constructs a standard multivariate Normal random vector generator.
NormalRVG(Vector mu, Matrix sigma)	Constructs a multivariate Normal random vector generator.
NormalRVG(Vector mu, Matrix sigma, double epsilon, RandomStandardNormalGenerator rnorm)	Constructs a multivariate Normal random vector generator.
NormalRVG(Vector mu, Matrix sigma, RandomStandardNormalGenerator rnorm)	Constructs a multivariate Normal random vector generator.

Method Summary

Modifier and Type	Method	Description
double[]	nextVector()	Gets the next random vector.
void	seed(long... seeds)	Seed the random number/vector/scenario generator to produce repeatable experiments.

Methods inherited from class java.lang.Object

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

Constructor Details

NormalRVG

public NormalRVG(Vector mu,
 Matrix sigma,
 double epsilon,
 RandomStandardNormalGenerator rnorm)

Constructs a multivariate Normal random vector generator.

Parameters:

mu - the mean

sigma - the covariance matrix

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

rnorm - a random standard Normal number generator

NormalRVG

public NormalRVG(Vector mu,
 Matrix sigma,
 RandomStandardNormalGenerator rnorm)

Constructs a multivariate Normal random vector generator.

Parameters:

mu - the mean

sigma - the covariance matrix

rnorm - a random standard Normal number generator

NormalRVG

public NormalRVG(Vector mu,
 Matrix sigma)

Constructs a multivariate Normal random vector generator.

Parameters:

mu - the mean

sigma - the covariance matrix

NormalRVG

public NormalRVG(int dim)

Constructs a standard multivariate Normal random vector generator.

Parameters:

dim - the dimension

Method Details

seed

public void seed(long... seeds)

Description copied from interface: Seedable

Seed the random number/vector/scenario generator to produce repeatable experiments.

Specified by:

seed in interface Seedable

Parameters:

seeds - the seeds

nextVector

public double[] nextVector()

Description copied from interface: RandomVectorGenerator

Gets the next random vector.

Specified by:

nextVector in interface RandomVectorGenerator

Returns:

the next random vector