mixSSG (version 2.1.1)

rssg: Simulating skewed sub-Gaussian stable random vector.

Description

Each skewed sub-Gaussian stable (SSG) random vector \(\bf{Y}\), admits the representation $$ {\bf{Y}} \mathop=\limits^d {\boldsymbol{\mu}}+\sqrt{P}{\boldsymbol{\lambda}}\vert{Z}_0\vert + \sqrt{P}{\Sigma}^{\frac{1}{2}}{\bf{Z}}_1, $$ where \({\boldsymbol{\mu}} \in {R}^{d} \) is location vector, \({\boldsymbol{\lambda}} \in {R}^{d}\) is skewness vector, \(\Sigma\) is a positive definite symmetric dispersion matrix, and \(0<\alpha \leq 2\) is tail thickness. Further, \(P\) is a positive stable random variable, \({Z}_0\sim N({0},1)\), and \({\bf{Z}}_1\sim N_{d}\bigl({\bf{0}}, \Sigma\bigr)\). We note that \(Z\), \(Z_0\), and \({\bf{Z}}_1\) are mutually independent.

Usage

rssg(n, alpha, Mu, Sigma, Lambda)

Value

simulated realizations of size \(n\) from the skewed sub-Gaussian stable distribution.

Arguments

n

the number of samples required.

alpha

the tail thickness parameter.

Mu

a vector giving the location parameter.

Sigma

a positive definite symmetric matrix specifying the dispersion matrix.

Lambda

a vector giving the skewness parameter.

Author

Mahdi Teimouri

Examples

n <- 4
alpha <- 1.4
Mu <- rep(0, 2)
Sigma <- diag(2)
Lambda <- rep(2, 2)
rssg(n, alpha, Mu, Sigma, Lambda)