We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone decompositions of the events in the sample space that correspond to the cumulative distribution function of the kth order statistic if they are measured by the ln,p-symmetric probability measure.We show that in each case distributions of the order statistics from ln,p-symmetric sample distribution can be represented as mixtures of skewed ln−ν,p-symmetric distributions, ν ∈ {1, . . . , n − 1}.
@article{bwmeta1.element.doi-10_1515_demo-2017-0013,
author = {K. M\"uller and W.-D. Richter},
title = {Exact distributions of order statistics from ln,p-symmetric sample distributions},
journal = {Dependence Modeling},
volume = {5},
year = {2017},
pages = {221-245},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_demo-2017-0013}
}
K. Müller; W.-D. Richter. Exact distributions of order statistics from ln,p-symmetric sample distributions. Dependence Modeling, Tome 5 (2017) pp. 221-245. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_demo-2017-0013/