Uniformly most powerful unbiased tests for the dispersion parameter of the Conway–Maxwell–Poisson distribution

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 t...

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Bibliographic Details
Published in:Statistics & probability letters 2023-05, Vol.196, p.109801, Article 109801
Main Authors: Bedbur, S., Kamps, U.
Format: Article
Language:English
Subjects:
Conway–Maxwell–Poisson distribution
Overdispersion
Underdispersion
Uniformly most powerful unbiased test
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2023.109801