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

• Main Authors: Müller K., Richter W.-D.
• Format: Article
• Language: English
• Published: De Gruyter 2017-08-01
• Series: Dependence Modeling
• Subjects: density generator; extreme value statistics; ln,p-dependence; measure-of-cone representation; skewed ln,p-symmetric distribution
• Online Access: https://doi.org/10.1515/demo-2017-0013

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}.