Smooth Flexible Models of Time-Dependent ArrivalsUsing One or More Process Realizations

摘要

Nonhomogeneous Poisson processes represent a large class of nonstationary stochastic point processes (e.g., arrivalprocesses) encountered in practice. We develop and evaluate a semiparametric method to estimate the mean-valuefunction of a nonhomogeneous Poisson process (NHPP) using one or more process realizations observed over afixed time interval. To approximate the mean-value function, the method exploits a specially formulated polynomialthat is constrained in least-squares estimation to be nondecreasing so the corresponding rate function is nonnegativeand smooth (continuously differentiable). Finally, a method for generating realizations from the fitted NHPP for usein simulation models is demonstrated.