Subset Selection Procedures for Poisson Processes and Some Applications to the Binomial and Multinomial Problems.

摘要

The Poisson process arises in many applications, especially, as a model for arrivals at a store, for arrivals of calls at a telephone exchange, for arrivals of radioactive particles at a Geiger counter, etc. In this paper, the problem of selecting a subset of k different Poisson processes including the best which is associated with the largest value of the mean rate is discussed. Some subset selection procedures are proposed and studied. An application of these procedures to the subset selection problem for the largest probability of a success of k binomial populations, whose parameters are unknown, is considered. Results are also applied to the problem of selecting the largest cell probability from a multinomial distribution, again the cell probabilities being unknown.