Estimating and Simulating Poisson Processes with Trends or Asymmetric Cyclic Effects

We present a heuristic that provides a nonparametric estimate of the mean-value function of a nonhomogeneous Poisson process having a long-term trend or some cyclic effect(s) that may lack sinusoidal symmetry over the corresponding cycle(s). This heuristic is a multiresolution-based method that allows one to estimate the overall long-term trend of the process at the lowest resolution and then add the details of the process associated with progressively smaller periodic components at progressively higher resolutions. In addition, we present an algorithm for generating realizations of nonhomogeneous Poisson processes with the estimated mean-value function in simulation experiments.

• Type: Conference
• Year: 1997
• Where: WSC
• Authors: Michael E. Kuhl, Halim Damerdji, James R. Wilson
• Keywords: Long-term Trend, Mean-value Function, Modeling And Simulation, Nonhomogeneous Poisson Process, WSC 1997