Pornpop Saengthong, Winai Bodhisuwan and Ampai Thongteeraparp

pp. 701 - 711

Abstract

The zero inflated negative binomial-Crack (ZINB-CR) distribution is a mixture of Bernoulli distribution and negative
binomial-Crack (NB-CR) distribution, which is an alternative distribution for the excessive zero counts and overdispersion.
In this paper, some properties of the ZINB-CR distribution are discussed. Statistical inference of the parameters is derived by
maximum likelihood estimation (MLE) and the method of moments (MM). Monte Carlo Simulations are used to evaluate the
performance of parameter estimation methods in term of mean squared error (MSE). An application of the distribution is
carried out on a sample of excess zero-count data. Simulation results show that the MLE method outperforms the MM
method in specific parameter values. Furthermore, the ZINB-CR provides a better fit compared to the zero inflated Poisson
(ZIP), the zero inflated negative binomial (ZINB) and the negative binomial-Crack (NB-CR) distributions.

Keywords

• zero inflated negative binomial-Crack distribution
• count data
• overdispersion
• excessive zero
• maximum likelihood estimation
• method of moments