Exact distributions of order statistics from ln,p-symmetric sample distributions

K. Müller, and W.-D. Richter. "Exact distributions of order statistics from ln,p-symmetric sample distributions." Dependence Modeling 5.1 (2017): 221-245. <http://eudml.org/doc/288356>.

@article{K2017,
abstract = {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\}.},
author = {K. Müller, W.-D. Richter},
journal = {Dependence Modeling},
keywords = {density generator; extreme value statistics; ln,p-dependence; measure-of-cone representation; skewed ln,p-symmetric distribution},
language = {eng},
number = {1},
pages = {221-245},
title = {Exact distributions of order statistics from ln,p-symmetric sample distributions},
url = {http://eudml.org/doc/288356},
volume = {5},
year = {2017},
}

TY - JOUR
AU - K. Müller
AU - W.-D. Richter
TI - Exact distributions of order statistics from ln,p-symmetric sample distributions
JO - Dependence Modeling
PY - 2017
VL - 5
IS - 1
SP - 221
EP - 245
AB - 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}.
LA - eng
KW - density generator; extreme value statistics; ln,p-dependence; measure-of-cone representation; skewed ln,p-symmetric distribution
UR - http://eudml.org/doc/288356
ER -