draw.multivariate.laplace: Pseudo-Random Number Generation under Multivariate Laplace...

In MultiRNG: Multivariate Pseudo-Random Number Generation

Description

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

f(x|μ,Σ,γ)=c\exp(-((x-μ)^{T}Σ^{-1}(x-μ))^{γ/2})

for -∞ < x < ∞ and c=\frac{γΓ(d/2)}{2π^{d/2}Γ(d/γ)}|Σ|^{-1/2}, Σ is symmetric and positive definite, where μ, Σ, and γ 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

MultiRNG documentation built on March 6, 2021, 1:06 a.m.