Combinatorics of geometrically distributed random variables: Left-to-right maxima

Abstract

Assume that the numbers x 1, …, x n are the output of n independent geometrically distributed random variables. The number x i is a left-to-right maximum if it is greater (or equal, for a variation) than x 1, …, x i−1 . A precise average case analysis is performed for the parameter ‘number of left-to-right maxima’. The methods include generating functions and a technique from complex analysis, called Rice's method. Some additional results are also given.