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

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.