Zero Inflated and Zero Truncated Negative Binomial – Weighted Garima Distributions for Modeling Count Data

Abstract

In this paper, we introduced models for zero infated and zero truncated based on the negative binomial-weighted Garima (NB-WG) distribution. The zero inflated negative binomial- weighted Garima (ZINB-WG) distribution is a discrete probability distribution for the excessive zero counts and overdispersion which is a mixture of Bernoulli distribution and negative binomial- weighted Garima (NB-WG) distribution. Meanwhile, a new zero truncated distribution named as the zero truncated negative binomial- weighted Garima (ZTNB-WG) distribution can be used when the response variable is the set of positive integers. Some properties of the two different versions of NB-WG distribution are discussed and the estimation of the parameters is derived by maximum likelihood method (MLE). In addition, the usefulness of the proposed distributions is illustrated by real data sets.