mfitstab.elliptical function

mfitstab.elliptical

estimates the parameters of a d-dimensional elliptically contoured stable distribution, see Teimouri et al. (2018).

mfitstab.elliptical(yy, alpha0, Sigma0, Mu0)

Arguments

• yy: vector of d-dimensional realizations
• alpha0: initial value of the tail index parameter to start the EM algorithm
• Sigma0: initial value of the dispersion matrix to start the EM algorithm
• Mu0: initial value of the location vector to start the EM algorithm

Returns

• alpha: estimated value of the tail index parameter

• Sigma: estimated value of the dispersion matrix

• Mu: estimated value of the location vector

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

Examples

# Here we follow for applying the EM algorithm to Z=(x1, x2)^T using the
# initial values alpha0=1, Sigma0=matrix(c(0.75,0.25,0.25,0.75),2,2), and
# Mu0=(0.5,0.5)^T.
library("stabledist")
x1<-urstab(100,1.2,0,1,2,0)
x2<-urstab(100,1.2,0,0.5,2,0)
z<-cbind(x1,x2)
mfitstab.elliptical(z,1,matrix(c(0.75,0.25,0.25,0.75),2,2),c(0.5,0.5))