Cpit goodness-of-fit tests for the power-law process

The Power-Law Process is the non homogeneous Poisson process for which the intensity is a power of time. In this paper, we propose a procedure to test the goodness-of-fit of the n first occurrence times of a random point process to the Power-Law Process, based on the Conditional Probability Integral Transformation of O'Reilly-Quesenberry. The new tests are compared through simulation to other tests proposed by Rigdon and Klefsjö-Kumar. It is known that these tests can have a very low power on some alternatives. The major interest of the CPIT tests is that their power is always greater than the previous for these alternatives. Moreover, they are equivalent to the best tests for large sample sizes.