Power bounds for a test of equality of trends in k independent power law processes

In this paper a procedure based on Bartlett statistic to test the equality of power-law parameters of k independent non-homogeneous Poisson processes is proposed. Simple approximations to the distribution of the test statistic under the null hypothesis as well as under any specified non-null hypothesis are given in the case of equal or unequal sample sizes. For several k and sample sizes values, exact test sizes estimated by Monte Carlo simulation are compared to nominal ones. In the case of equal sample sizes approximate bounds for the power function are given, and a table is provided in order to determine the smallest size of each sample needed to guarantee a fixed power level.