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

Exact distributions of order statistics from ln,p-symmetric sample distributions AbstractWe 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}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

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

Müller, K.; Richter, W.-D.
Dependence Modeling , Volume 5 (1): 25 – Aug 28, 2017
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Publisher
de Gruyter
Copyright
© 2017
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2017-0013
Publisher site
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Abstract

AbstractWe 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}.

Journal

Dependence Modeling – de Gruyter

Published: Aug 28, 2017

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