Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data

Given a finite time horizon that has been partitioned into subintervals over which event counts have been accumulated for multiple realizations of a population NonHomogeneous Poisson Process (NHPP), this paper develops point and confidence-interval estimators for the cumulative intensity (or mean value) function of the population process evaluated at each subinterval endpoint. As the number of realizations tends to infinity, each point estimator is strongly consistent and the corresponding confidence-interval estimator is asymptotically exact. If the NHPP has a piecewise constant intensity (rate) function, then the proposed point and confidence-interval estimators for the cumulative intensity function are valid over the entire time horizon and not just at the subinterval endpoints; and in this case algorithms are presented for generating event times from the estimated NHPP. Event count data from a call center illustrate the point and interval estimators. 1