Sequential Probability Ratio Tests for the Shape Parameter of a Nonhomogeneous Poisson Process

Sequential probability ratio tests for the shape parameter of one or more nonhomogeneous Poisson processes, with power intensity functions, are provided. The tests can be performed when the scale parameter is an unknown nuisance parameter; the effective loss of not knowing the scale parameter is one observation per process. The resulting tests can be expressed in terms of the maximum likelihood estimators of the shape parameters for the usual fixed sample procedure. A further advantage of the present approach is that the scale parameters for different processes, in the multiple sample procedures, need not be equal. Approximations for the operating characteristic function and the average sample number are provided.