Empirical‐distribution‐function goodness‐of‐fit tests for discrete models

Abstract

Abstract We present a simple framework for studying empirical‐distribution‐function goodness‐of‐fit tests for discrete models. A key tool is a weak‐convergence result for an estimated discrete empirical process, regarded as a random element in some suitable sequence space. Special emphasis is given to the problem of testing for a Poisson model and for the geometric distribution. Simulations show that parametric bootstrap versions of the tests maintain a nominal level of significance very closely even for small samples where reliance upon asymptotic critical values is doubtful.