Discrete Compound Poisson Processes and Tables of the Geometric Poisson Distribution

摘要

A concise summary of the salient properties of discrete Poisson processes, with emphasis on comparing the geometric and logarithmic Poisson processes. The geometric Poisson process is particularly convenient when the analyst is interested in a simple model for the time between events--as in simulation. The logarithmic Poisson process is more convenient in analytical models in which the state probabilities are required. State probabilities of the geometric Poisson process are given for 176 sets of parameter values. New discrete compound Poisson processes are also introduced. These processes have properties that are particularly relevant when the summation of several different Poisson processes is to be analyzed. This study provides the theoretical foundation for extending RAND'S base stockage policy for recoverable items to more than one echelon (depot and base). To make the extension computationally feasible, the logarithmic Poisson description of demand was substituted for the geometric Poisson assumption used previously. (Author)