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

Assume that the numbers x1, …, xn are the output of n independent geometrically distributed random variables. The number xi is a left-to-right maximum if it is greater (or equal, for a variation) than x1, …, xi−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 Riceʹs method. Some additional results are also given.