rmggd function

Simulate from a Multivariate Generalized Gaussian Distribution

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

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.

Returns

A matrix with $p$ columns and n rows.

Details

A sample from a centered MGGD with dispersion matrix $\Sigma$

and shape parameter $\beta$ can be generated using:

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 $2$.

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)

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. tools:::Rd_expr_doi("10.1080/03610929808832115")

See Also

dmggd: probability density of a MGGD..

estparmggd: estimation of the parameters of a MGGD.

Author(s)

Pierre Santagostini, Nizar Bouhlel