A Novel Discrete Probability Distribution with Theoretical and Inferential Insights: Cutting-Edge Approaches to Sustainable Dispersion Data Modeling

As real-world data becomes increasingly complex, there is a growing need for advanced probability models to support sustainable discrete data analysis. This study presents a novel and flexible extension of the discrete Gompertz distribution, developed within the framework of the half-logistic model. Named the discrete Gompertz half-logistic (DGzHLo) model, this new formulation enhances the adaptability of existing discrete distributions to better capture intricate data patterns. To understand its theoretical foundation, key mathematical and statistical properties are examined, including the probability mass function, cumulative distribution function, reliability function, and hazard rate function. Measures such as dispersion, skewness, and kurtosis offer insights into the model's behavior, while entropy and order statistics further reveal its structural characteristics. The model's parameters are estimated using the maximum likelihood estimation method, and a thorough simulation study assesses the accuracy and efficiency of the estimators across various sample sizes. To illustrate its practical relevance, the model is applied to three real-world datasets, demonstrating its superior flexibility and robustness in capturing complex data structures compared to existing models. These findings underscore the DGzHLo model's effectiveness in advancing discrete data modeling and analysis.