Inference on parameter β of the Generalized Negative Binomial Distribution

In this paper, we propose a generalized likelihood ratio test to discern whether a set of data fits a Negative Binomial as a particular case of the Generalized Negative Binomial Distribution(GNBD). The test attempts to differentiate the GNBD from Negative Binomial (NBD) distribution when fitting discrete data. A Monte Carlo simulation study was performed to investigate the power and the size of the proposed test, and results shows good performance in power and size under moderate sample sizes of the LRT test for testing hypotheses on parameter β of the Generalized Negative Binomial Distribution. A Parametric Bootstrap for investigating the distribution of parameter β of the GNBD and a Bayesian approach for obtaining the posterior distribution of the GNBD parameters were also implemented. In order to illustrate the proposed methodology, we included two cases: a dataset of an entomological study on mosquitoes of malaria and another study on species of Malaysian butterflies.