Estimation of Selected Parameters in Non-Homogeneous Poisson Processes.
Douglas E. Huffman · TigerPrints (Clemson University) · 1975
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 .