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

Multiplicative-binomial distribution is one of the distributions that allows for over-dispersion, and underdispersion 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.