Abstract

The problem of comparing the means of two independent Poisson distributions has been addressed in the literature. A generalization of the Poisson distribution to accommodate over- and under-dispersion in the data is the two-parameter Poisson distribution developed by Conway and Maxwell. This distribution has nice properties, and it includes geometric, Poisson and binomial distributions as its special cases. The present work considers the problem of comparing the means of two independent reparametrized Conway-Maxwell Poisson distributions assuming the dispersion parameter to be known. The proposed test procedures make use of the conditional, exact, asymptotic and likelihood ratio test approaches. The test statistic under various approaches is derived, and the respective powers and effect sizes are evaluated and compared through a simulation study. A numerical illustration of the applicability of the tests is provided through real-life data.

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