| rssg {mixSSG} | R Documentation |
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)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)