Neutrosophic Negative Binomial Hurdle Models for Overdispersed Zero-Inflated Count Data

The Negative Binomial Hurdle (NBH) model stands as a preeminent statistical framework for analyzing overdispersed count data characterized by a preponderance of zero observations. Its two-part structure (decoupling the probability of a zero outcome from the distribution of positive counts) provides a powerful and intuitive mechanism for capturing complex data-generating processes. However, the conventional NBH model, alongside its classical counterparts, operates under the stringent assumption of precisely defined parameters, a condition often violated in real-world empirical contexts. Data is frequently imbued with inherent indeterminacy, stemming from measurement inaccuracies, ambiguous classification criteria, subjective judgment, or intrinsic system volatility. This paper introduces the Neutrosophic Negative Binomial Hurdle (NNBH) model, a novel generalization that integrates the principles of neutrosophic logic into the hurdle framework. By formulating key parameters (the hurdle probability, the count rate, or both) as neutrosophic numbers, the proposed model quantifies indeterminacy through interval-based estimates, thereby offering a more honest and robust representation of underlying uncertainties. We formally derive the model’s probability mass function, likelihood, and fundamental statistical properties. Parameter estimation is achieved through an adapted Neutrosophic Maximum Likelihood Estimation (NMLE) algorithm. The model’s superior flexibility and performance are unequivocally demonstrated through an extensive simulation study and a compelling real-world application to healthcare utilization data, where it yields a more nuanced and informative fit than its classical and partially neutrosophic predecessors. This work provides a critical new analytical tool for researchers and practitioners in public health, economics, and industrial engineering who must derive inferences from complex, vague, and overdispersed count processes.