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Abstract This paper introduces a novel modification of the negative binomial distribution, which serves as a generalization encompassing both negative binomial and zero-inflated negative binomial distributions. This innovative distribution offers flexibility by accommodating an arbitrary number of inflation points at various locations. The paper explores key distributional properties associated with this modified distribution. Additionally, this study proposes several estimators designed to obtain estimates for the unknown parameters. Furthermore, the paper introduces a new count regression model that utilizes the modified distribution. To assess the performance of the proposed distribution and the count regression model, a comprehensive Monte Carlo simulation study is conducted. In the final stage of the paper, a real-world dataset is scrutinized to ascertain the superiority of the proposed model. This empirical analysis contributes to validating the practical applicability and effectiveness of the newly introduced distribution in comparison to existing models.
Abusaif et al. (Fri,) studied this question.