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

Müller K. () and Richter W.-D. ()
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Müller K.: University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany
Richter W.-D.: University of Rostock, Institute of Mathematics, Ulmenstraße 69, Haus 3, 18057 Rostock, Germany

Dependence Modeling, 2017, vol. 5, issue 1, 221-245

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}.

Keywords: density generator; extreme value statistics; ln; p-dependence; measure-of-cone representation; skewed ln; p-symmetric distribution (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:5:y:2017:i:1:p:221-245:n:13

DOI: 10.1515/demo-2017-0013

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