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

• Main Authors: Martin Tejkal, Zuzana Hübnerová
• Format: Article
• Language: English
• Published: Mendel University Press 2018-01-01
• Series: Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis
• Subjects: Poisson distribution; negative binomial distribution; ANOVA; <i>F</i>‑test statistic; generalized linear model; likelihood ratio
• Online Access: https://acta.mendelu.cz/66/4/1025/
• ISSN: 1211-8516; 2464-8310

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.