Distorted Poisson Processes.
Abstract
A new family of Poisson cluster processes, called distorted Poisson (DP) processes, is introduced and shown to generalize the (stationary) Gauss-Poisson family. Representations of the DP processes in terms of the probability generating functional are developed and utilized as tools to derive various qualitative and quantitative properties of the DP family. The qualitative properties include: stationarity, orderliness, closure under superposition, translation and deletion, infinite divisibility, mixing, ergodicty. The quantitative properties are: moments; variance and covariance functions; index of dispersion; waiting time distributions; recursion formulas for count probabilities; asymptotic normality of counts. Applications of the DP model are discussed, including its role in connection with robust estimation in a Poisson process. The role of the DP family is assessed in general and in comparison with the Bartlett-Lewis and Neyman-Scott families of Poisson cluster processes. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1976
- Accession Number
- ADA026317
Entities
People
- P. F. Thall
- Robert Serfling
Organizations
- Florida State University