Exploring the Potential of the Kumaraswamy Discrete Half-Logistic Distribution in Data Science Scanning and Decision-Making

Data science often employs discrete probability distributions to model and analyze various phenomena. These distributions are particularly useful when dealing with data that can be categorized into distinct outcomes or events. This study presents a discrete random probability model, supported by non-negative integers, formulated from the well-established Kumaraswamy family through a recognized discretization method, preserving the survival function’s functional structure. Various significant statistical properties like hazard rate function, crude moments, index of dispersion, skewness, kurtosis, quantile function, L-moments, and entropies are derived. This new probability mass function allows for the analysis of asymmetric dispersion data across different kurtosis forms, including mesokurtic, platykurtic, and leptokurtic distributions. Furthermore, this model effectively handles excess zeros, under and over dispersion commonly encountered in diverse fields. Additionally, the hazard rate function demonstrates considerable flexibility, encompassing monotonic decreasing, bathtub, monotonously increasing, and bathtub-constant failure rate characteristics. Following the theoretical introduction of this new discrete model, model parameters are estimated through maximum likelihood estimation, with a subsequent discussion on the performance of this technique through a simulation study. Finally, three real-world applications employing count data demonstrate the significance and adaptability of this novel discrete distribution.