Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors

Abstract

The relative frequency of order statistics is investigated for independent and identically distributed (i.i.d.) random variables. Specifically, it is shown that the probability   is no less than the probability   at any point ≧  when   where  denotes the -th order statistic of an i.i.d. discrete random vector and  depends on the population probability distribution. A similar result for i.i.d. continuous random vectors is also presented.