Order statistics and exceedances for some models of INID random variables

Abstract

Order statistics and exceedances for some general models of independent but not necessarily identically distributed (INID) random variables are considered. The distributions of order statistics from INID sample are described in terms of symmetric functions. Some exceedance models based on order statistics from INID random variables are considered, the limit distributions of exceedance statistics are obtained. For the model of INID random variables referred as $F^{\alpha}$-scheme introduced by Nevzorov (Zapiski Nauchnykh Seminarov LOMI 142 (1985) 109–118) the limiting distribution of exceedance statistic has been derived. This distribution is expressed in terms of permutations with inversions, Gaussian Hypergeometric function and incomplete beta functions.