This thesis considers the problems of testing equality of two (homogeneous) Poisson processes, two nonhomogeneous Poisson processes and two Bernoulli processes based on inverse sampling. Three sampling procedures are considered:
1. Observe the first process until s events occur and then observe the second process until s events occur.
2. Observe the two processes concurrently until s events occur in the first process.
3. Observe the two processes concurrently until s events occur for the first time in one of them.
Under each sampling procedure, likelihood ratio and the other tests are derived and the number of samples required to guarantee a prescribed power is obtained. Comparison of the processes are also made from a Bayesian viewpoint.
