Some tests for a poisson process and their powers with respect to trend in the intensity

Recently many authors have worked on Wei bull process in the area of modelling and analysis. Much less work is done in the area of testing of hypothesis. In this article, some tests for testing the Poisson process against a class of Wei bull process based on the conditional distribution of observations given the sufficient statistic, are proposed. The percentage points of the distributions of the proposed test statistics are simulated. The powers of the tests under alternatives are computed by Monte Carlo method. It is seen that the suggested tests perform well for decreasing intensities.