Comparison of Approaches to Testing Equality of Expectations Among Samples from Poisson and Negative Binomial Distribution

Martin Tejkal and Zuzana Hübnerová
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Martin Tejkal: Department of Econometrics, Faculty of Military Leadership, University of Defence in Brno, Kounicova 65, Brno, Czech Republic
Zuzana Hübnerová: Department of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, Brno, Czech Republic

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 2018, vol. 66, issue 4, 1025-1034

Abstract: The paper deals with testing of the hypothesis of equality of expectations among p samples from Poisson or negative binomial distribution. a comparison of two main approaches is carried out. The first approach is based on transforming the samples from either Poisson or negative binomial distribution in order to achieve normality or variance stability, and then testing the hypothesis of equality of expectations via the F-test. In the second approach, test statistics coming from the theory of maximum likelihood appearing in generalised linear models framework, specially designed for testing the hypothesis among samples from the respective distributions (Poisson or negative binomial), are used. The comparison is done graphically, by plotting the simulated power functions of the test of the hypothesis of equality of expectations, when first or second approach was used. Additionally, the relationship between the power functions obtained via the respective approaches and sample sizes is studied by evaluating the respective power functions as functions of a sample size numerically.

Keywords: Poisson distribution; negative binomial distribution; ANOVA; F-test statistic; generalized linear model; likelihood ratio; score statistic; variance stabilizing transformation; Yeo-Johnson transformation; power function (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:mup:actaun:actaun_2018066041025

DOI: 10.11118/actaun201866041025

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