rmtd: Simulate from a Multivariate t Distribution

In multvardiv: Multivariate Probability Distributions, Statistical Divergence

Simulate from a Multivariate t Distribution

Description

Produces one or more samples from the multivariate (p variables) t distribution (MTD) with degrees of freedom nu, mean vector mu and correlation matrix Sigma.

Usage

rmtd(n, nu, mu, Sigma, tol = 1e-6)

Arguments

n	integer. Number of observations.
nu	numeric. The degrees of freedom.
mu	length p numeric vector. The mean vector
Sigma	symmetric, positive-definite square matrix of order p. The correlation matrix.
tol	tolerance for numerical lack of positive-definiteness in Sigma (for mvrnorm, see Details).

Details

A sample from a MTD with parameters \nu, \boldsymbol{\mu} and \Sigma can be generated using:

\displaystyle{\mathbf{X} = \boldsymbol{\mu} + \mathbf{Y} \sqrt{\frac{\nu}{u}}}

where Y is a random vector distributed among a centered Gaussian density with covariance matrix \Sigma (generated using mvrnorm) and u is distributed among a Chi-squared distribution with \nu degrees of freedom.

Value

A matrix with p columns and n rows.

Author(s)

Pierre Santagostini, Nizar Bouhlel

References

S. Kotz and Saralees Nadarajah (2004), Multivariate t Distributions and Their Applications, Cambridge University Press.

See Also

dmtd: probability density of a MTD.

estparmtd: estimation of the parameters of a MTD.

Examples

nu <- 3
mu <- c(0, 1, 4)
Sigma <- matrix(c(1, 0.6, 0.2, 0.6, 1, 0.3, 0.2, 0.3, 1), nrow = 3)
x <- rmtd(10000, nu, mu, Sigma)
head(x)
dim(x)
mu; colMeans(x)
nu/(nu-2)*Sigma; var(x)

multvardiv documentation built on April 3, 2025, 6:08 p.m.