A test for superadditivity of the mean value function of a non-homogeneous Poisson process

Let N(t) be a non-homogeneous Poisson process with mean value function [Lambda](t) and rate of occurrence [lambda](t). We propose a conditional test of the hypothesis that the process is homogeneous, versus alternatives for which the mean value function is superadditive. Specific models leading to superadditivity are presented, and the superadditive test is compared, on the basis of consistency and asymptotic relative efficiency, with the Cox-Lewis test, the latter being directed to alternatives where [lambda](t) is increasing.