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

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Müller K., Richter W.-D.

Dependence Modeling

2017

tom 5

nr 1

221-245

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}.

Ograniczanie wyników

1 Dependence Modeling

1 Müller K.

1 Richter W.-D.

1 2017

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