Discrete Extension of the Inverse Weibull Distribution: Theory and Decision-Making for Count Data in Sustainability Analysis

In the realm of sustainability, lifetimes are often modeled with discrete measurements due to finite precision, lacking a continuous representation. Despite the inherent continuity in device or patient lifetimes, it is reasonable to consider their observations as stemming from a discretized distribution derived from a continuous model. This study introduces a discrete random probability model based on non-negative integers, formulated from the established Kumaraswamy family using recognized discretization methods while preserving the survival function’s structure. The generated discrete model is called the Kumaraswamy discrete inverse Weibull. Various statistical properties, such as the hazard rate function, moments, dispersion index, skewness, kurtosis, quantile function, L-moments, and entropies, are explored. The new discrete model’s parameters are estimated using maximum likelihood estimation, followed by a discussion on its performance in a simulation study. Additionally, three real-world sustainability applications using count data showcase the importance and versatility of this innovative discrete distribution.