rssg: Simulating skewed sub-Gaussian stable random vector.

In mixSSG: Clustering Using Mixtures of Sub Gaussian Stable Distributions

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{μ}}+√{P}{\boldsymbol{λ}}\vert{Z}_0\vert + √{P}{Σ}^{\frac{1}{2}}{\bf{Z}}_1,

where {\boldsymbol{μ}} \in {R}^{d} is location vector, {\boldsymbol{λ}} \in {R}^{d} is skewness vector, Σ is a positive definite symmetric dispersion matrix, and 0<α ≤q 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}}, Σ\bigr). We note that Z, Z_0, and {\bf{Z}}_1 are mutually independent.

Usage

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

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.

Value

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

Author(s)

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)

mixSSG documentation built on Sept. 11, 2022, 5:06 p.m.