On a Distribution Associated with Certain Stochastic Processes

Abstract

The distribution discussed is (a) the total number of games lost by the ruined gambler starting withamonetary units against an infinitely rich adversary in the classical ruin problem; (b) the total size of an epidemic in an infinite population starting withacases and with constant probabilities of infection and recovery; (c) the number of customers served in a busy period (starting withacustomers) of the queueM/M/1. These derivations, the relationships between them and various properties of the distribution are discussed.