Order statistics for nonidentically distributed variables and permanents

Abstract

Theory of permanents provides an effective tool in dealing with order statistics corresponding to random variables which are independent but possibly nonidentically distributed. This is illustrated by giving a characterization of symmetric random variables in terms of order statistics and by generalizing some known recurrence relations. It is shown that the distribution function of one or more order statistics can be represented in terms of permanents and this fact combined with the Alexandroff inequality is used to demonstrate the log-concavity of certain sequences. The case of order statistics corresponding to independent exponential random variables is considered and the m.g.f. and moments of an order statistic and those of the range are derived explicitly.