MultiRNG (version 1.2.4)

draw.multivariate.laplace: 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

# NOT RUN {
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)
# }
# NOT RUN {
apply(mydata,2,mean)-mu.vec
cor(mydata)-cmat
# }