draw.multivariate.laplace {MultiRNG}

Pseudo-Random Number Generation under Multivariate Laplace Distribution

Description

This function implements pseudo-random number generation for a multivariate Laplace (double exponential) distribution with pdf

f(x|\mu,\Sigma,\gamma)=c\exp(-((x-\mu)^{T}\Sigma^{-1}(x-\mu))^{\gamma/2})

for -\infty < x < \infty and c=\frac{\gamma\Gamma(d/2)}{2\pi^{d/2}\Gamma(d/\gamma)}|\Sigma|^{-1/2}, \Sigma is symmetric and positive definite, where \mu, \Sigma, and \gamma are the mean vector, the variance-covariance matrix, and the shape parameter, respectively.

Usage

draw.multivariate.laplace(no.row,d,gamma,mu,Sigma)

Arguments

no.row

Number of rows to generate.

d

Number of variables to generate.

gamma

Shape parameter.

mu

Vector of means.

Sigma

Variance-covariance matrix.

Value

A no.row \times d matrix of generated data.

References

Ernst, M. D. (1998). A multivariate generalized Laplace distribution. Computational Statistics, 13, 227-232.

See Also

generate.point.in.sphere

Examples

cmat<-matrix(c(1,0.2,0.3,0.2,1,0.2,0.3,0.2,1), nrow=3, ncol=3)
mu.vec=c(0,3,7)
mydata=draw.multivariate.laplace(no.row=1e5,d=3,gamma=2,mu=mu.vec,Sigma=cmat)

apply(mydata,2,mean)-mu.vec
cor(mydata)-cmat