mfitstab.ustat {alphastable} | R Documentation |
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
.
mfitstab.ustat(u,m,method=method)
u |
an |
m |
number of masses located on unit circle in |
method |
integer values 1 or 2, respectively, corresponds to the method given by Teimouri et al. (2017) and Mohammadi et al. (2015) |
alpha |
estimated value of tail index |
mass |
estimated value of discrete spectral measure |
Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah
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.
# 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)