mfitstab.ustat {alphastable}

mfitstab.ustat

Description

estimates the parameters of a strictly bivariate stable distribution using approaches proposed by Mohammadi et al. (2015)<doi.org/10.1007/s00184-014-0515-7> and Teimouri et al. (2017)<doi.org/10.1155/2017/3483827>. The estimated parameters are tail index and discretized spectral measure on m equidistant points located on unit sphere in R^2.

Usage

mfitstab.ustat(u,m,method=method)

Arguments

u

an n by 2 vector of observations

m

number of masses located on unit circle in R^2

method

integer values 1 or 2, respectively, corresponds to the method given by Teimouri et al. (2017) and Mohammadi et al. (2015)

Value

alpha

estimated value of tail index

mass

estimated value of discrete spectral measure

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

References

Mohammadi, M., Mohammadpour, A., and Ogata, H. (2015). On estimating the tail index and the spectral measure of multivariate alpha-stable distributions, Metrika, 78(5), 549-561.

Nolan. J. P. (2013). Multivariate elliptically contoured stable distributions: theory and estimation, Computational Statistics, 28(5), 2067-2089.

Teimouri, M., Rezakhah, S., and Mohammadpour, A. (2017). U-Statistic for multivariate stable distributions, Journal of Probability and Statistics, https://doi.org/10.1155/2017/3483827.

Examples

# Here, for example, we are interested to estimate the parameters of a bivariate
# stable distribution. For this, two sets of n=400 iid realizations which are
# assumed to distributed jointly as a strictly bivariate stable distribution with
# tail index alpha=1.2 are simulated. Considering m=4, masses of the discrete spectral
# measure are addressed by s_j=(cos(2*pi(j-1)/m), sin (2*pi(j-1)/m)); for j=1,...,4.
library("nnls")
x1<-urstab(400,1.2,-0.50,1,0,0)
x2<-urstab(400,1.2,0.50,0.5,0,0)
z<-cbind(x1,x2)
mfitstab.ustat(z,4,1)