rmggd {mggd}

Simulate from a Multivariate Generalized Gaussian Distribution

Description

Produces one or more samples from a multivariate (p variables) generalized Gaussian distribution (MGGD).

Usage

rmggd(n = 1 , mu, Sigma, beta, tol = 1e-6)

Arguments

n

integer. Number of observations.

mu

length p numeric vector. The mean vector.

Sigma

symmetric, positive-definite square matrix of order p. The dispersion matrix.

beta

positive real number. The shape of the distribution.

tol

tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma.

Details

A sample from a centered MGGD with dispersion matrix \Sigma and shape parameter \beta can be generated using:

\displaystyle{X = \tau \ \Sigma^{1/2} \ U}

where U is a random vector uniformly distributed on the unit sphere and \tau is such that \tau^{2\beta} is generated from a distribution Gamma with shape parameter \displaystyle{\frac{p}{2\beta}} and scale parameter 2.

This property is used to generate a sample from a MGGD.

Value

A matrix with p columns and n rows.

Author(s)

Pierre Santagostini, Nizar Bouhlel

References

E. Gomez, M. Gomez-Villegas, H. Marin. A Multivariate Generalization of the Power Exponential Family of Distribution. Commun. Statist. 1998, Theory Methods, col. 27, no. 23, p 589-600. doi:10.1080/03610929808832115

See Also

dmggd: probability density of a MGGD..

estparmggd: estimation of the parameters of a MGGD.

Examples

mu <- c(0, 0, 0)
Sigma <- matrix(c(0.8, 0.3, 0.2, 0.3, 0.2, 0.1, 0.2, 0.1, 0.2), nrow = 3)
beta <- 0.74
rmggd(100, mu, Sigma, beta)