Estimation and testing of an exponential polynomial rate function within the nonstationary Poisson process

This paper presents a numerical method of statistical inference which overcomes some mathematical difficulties encountered in the nonstationary Poisson process by taking full advantage of modern computing equipment. The maximum likelihood estimator of an exponential polynomial rate function has moments equal to the corresponding sums of powers of the observed event times. A numerieal determination of this function is demonstrated. The information matrix, a simple function of the moments of the rate function, can also be estimated by the sums of powers. Finally, a goodness-of-fit test is derived from the relation between sums of powers of event times and moments of the rate function. Computer programs which perform all the necessary calculations have been prepared and are available from the author.