Date of Award

5-1975

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

First Advisor

Paul T. Holmes

Second Advisor

John Kenelly

Third Advisor

A. E. Schwertz

Abstract

In this paper a nonparametric approach is used to find estimates of certain parameters in non-homogeneous Poisson processes . The approach is nonparametric becau se the intensity function is not assumed to have a particular functional form. The sampling procedure used is to observe a random sample of size k of the process on the interval [O , T] , where T is a fixed positive constant . To motivate the procedures used to estimate the intensity function , the Rao- Blackwell estimate of the mean value function is given . Three possible estimates of the intensity function are given , and asymptotic (k+∞) properties are obtained for each . Three possible solutions to the peak rate problem are offered , and again asymptotic properties are obtained for each . Finally , estimates for the mean and for the population quantiles of a related density funciton are obtained .

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