mdstab.elliptical function

mdstab.elliptical

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).

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

Returns

a numeric value

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.

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

Note

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

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))