Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation

Abstract

Multiplicative-binomial distribution is one of the distributions that allows for over-dispersion and under-dispersion relative to the standard binomial distribution. It will be shown that the multiplicative-binomial distribution can be a very useful model for these situations. Moreover, the confidence interval for the parameters of the multiplicative-binomial distribution is investigated by the profile likelihood methods. The first four moments and simulation procedures for generating data from the multiplicative-binomial distribution using R-software are given. By using four applications to simulated and real data it is shown that the multiplicative-binomial distribution is the same as or outperforming the standard binomial and beta-binomial distributions.

Keywords

• binomial distribution; likelihood ratio test; over-dispersion; profile likelihood; zero-inflated data.