Abstract
Uniformly most powerful unbiased tests for one-sided hypotheses about the dispersion parameter of the Conway–Maxwell–Poisson distribution are derived by utilizing the exponential family structure, and it is shown how to obtain the critical values of the relevant test statistics via simulation. The tests, which do not require parameter estimators, are applied to several real data sets from the literature to statistically confirm under- or overdispersion, giving evidence against the common Poisson model for count data.
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