Use of an empirical probability generating function for testing a Poisson model |
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Authors: | Miguel Nakamura Victor Prez-Abreu |
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Institution: | Miguel Nakamura,Victor PÉrez-Abreu |
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Abstract: | 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 anlyzing count data are promising. |
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Keywords: | Goodness of fit Poisson index of dispersion distribution for counts smooth goodness-of-fit test V-statistic |
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