The “Straightforward” Nature of Arrival Rate Estimation?

Abstract

How one estimates the parameter in a Poisson process depends critically on the rule used to terminate the sampling period. For observation until the kth arrival, or observation until time t, well-known maximum likelihood estimators (MLEs) can be used, although they can be biased if the sampling period is such that the expected number of arrivals is small. If one uses a stopping rule such as “observe until the kth arrival or time t,” the form of the MLE becomes more complex. In the latter case, it appears a simple ad hoc estimator outperforms its MLE competitor.

Originally published in The American Statistician, Volume 52, Number 4 in 1998, this work was one of the first papers that used APPL as its primary research tool. APPL was useful in finding many aspects that solidified this work, to include simulations of random processes, likelihood function calculations, and finding moments with the Mean and Variance procedures.