Bootstrap based goodness of fit tests for the generalized Poisson model

Due to its versatile natuie, the Generalized Poisson distribution (GPD) of Consul and Jain (1973) has been an object of sustained interest Howeer, apart from the classical x$^2$test ith its inherent problems, there is a paucity of genuine goodness of fit tests foi checking the GPD model on the basis of given data In this paper we study empirical distribution function based tests for the GPD model A key tool is a weak convergence result for an estimated (discrete) empirical process, regarded as a random element in some suitable sequence space. A parametric bootstrap version of the procedure is shown to maintain a desired level of significance very closely even for small sample sizes The test is applied to data sets of frequencies of the duration of atmospheric circulation patterns.