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

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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)

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}.

Suggested Citation

  • Müller K. & Richter W.-D., 2017. "Exact distributions of order statistics from ln,p-symmetric sample distributions," Dependence Modeling, De Gruyter, vol. 5(1), pages 221-245, August.
    • Handle: RePEc:vrs:demode:v:5:y:2017:i:1:p:221-245:n:13
    DOI: 10.1515/demo-2017-0013
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    References listed on IDEAS

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