mfitstab.ustat {alphastable} R Documentation

## 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

### 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)


[Package alphastable version 0.2.1 Index]