Distorted Poisson Processes.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
Pagination or Media Count:
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
- Statistics and Probability