Theoretical Statistics and Mathematics Unit, ISI Delhi

Dependence Orderings for Generalized Order Statistics

by Baha-Eldin Khaledi and Subhash Kochar

Generalized order statistics (g{\bf OS}s) unify the study of order statistics, record values, k-records, Pfeifer's records and several other cases of ordered random variables. In this paper we consider the problem of comparing the degree of dependence between a pair of g{\bf OS}s thus extending the recent work of Averous, Genest and Kochar (2005). It is noticed that as in the case of ordinary order statistics, copula of g{\bf OS}s is independent of the parent distribution. For this comparison we consider the notion of more regression dependence or more stochastic increasing. It follows that under some conditions, for $i < j$, the dependence of the $j$th generalized order statistic on the $i$th generalized order statistic decreases as $i$ and $j$ draw apart. We also obtain a close form expression for the Kendall's coefficient of concordance between a pair of record values.

isid/ms/2005/02 [fulltext]

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