Goodness of fit test for discrete random variables

In this paper, a goodness of fit (gof) test for discrete random variables is studied. For the test, the empirical process gof test constructed based on the Khmaladze transformation method is considered to remove the parameter estimation effect. Further, the approach of the continuous extension of discrete random variables introduced in Denuit and Lambert (2005) is adopted. It is shown that under regularity conditions, the transformed empirical process weakly converges to a standard Brownian motion. As a gof test based on this result, the maximum entropy type test designed by Lee et al. (2011) is considered. As with the empirical process gof test, Vasicek’s entropy test is also considered and a properly modified version, whose limiting distribution is unaffected by the choice of parameter estimates, is provided. Simulation results are provided for illustration.