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.
Keywords
zero inflated distribution, zero truncated distribution, negative binomial-weighted Garima distribution, count data, maximum likelihood estimation