mdstab.elliptical {alphastable}

mdstab.elliptical

Description

computes the probability density function of a d-dimensional elliptically contoured stable distribution at a given point in R^{d}, see Teimouri et al. (2018).

Usage

mdstab.elliptical(x, alpha, Sigma, Mu)

Arguments

x

vector of real values in R^d

alpha

tail index parameter

Sigma

d by d positive definite dispersion matrix

Mu

location vector in R^d

Value

a numeric value

Note

mdstab.elliptical() computes the probability density function of an d-dimensional elliptically contoured stable distribution using either asymptotic series or Monte Carlo approximation.

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

References

Teimouri, M., Rezakhah, S., and Mohammadpour, A. (2018). Parameter estimation using the EM algorithm for symmetric stable random variables and sub-Gaussian random vectors, Journal of Statistical Theory and Applications, 17(3),1-20.

Examples

# In the following example, we compute the pdf of a two-dimensional elliptically contoured
# stable distribution with parameters alpha=1.3, Sigma=matrix(c(1,.5,.5,1),2,2), and mu=(0,0)^T.
library("stabledist")
mdstab.elliptical(c(5,5),1.2,matrix(c(1,0.5,0.5,1),2,2),c(0,0))