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

Dependence Modeling (2017)

- Volume: 5, Issue: 1, page 221-245
- ISSN: 2300-2298

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topK. 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 -

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