On outstanding values in a sequence of random variables

Abstract

A sequence {Xn} of independent and identically distributed (i.i.d.) random variables is considered. Outstanding values in the sequence are those that strictly exceed values preceding them. Let Ln be the index of the n-th outstanding value. Limit theorems are given for the sequences {Mathematical expression} and {Ln} and {δn} where δn=Ln-Ln-1. A characterization of the exponential distribution in terms of the sequence {Mathematical expression} is also given. © 1969 Springer-Verlag.