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Use of an empirical probability generating function for testing a Poisson model. (English) Zbl 0779.62039

Summary: We present a test of the fit to a Poisson model based on the empirical probability generating function (epgf). We derive the limiting distribution of the test under the Poisson hypothesis and show that a rescaling of it is approximately independent of the mean parameter in the Poisson distribution. When inspected under a simulation study over a range of alternative distributions, we find that this test shows reasonable behaviour compared to other goodness-of-fit tests like the Poisson index of dispersion and smooth test applied to the Poisson model. These results illustrate that epgf-based methods for analyzing count data are promising.

MSC:

62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
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