A new bivariate Kumaraswamy discrete Lindley model: theory and multidisciplinary data analysis

This study presents the bivariate Kumaraswamy discrete Lindley distribution, developed via a trivariate minimization framework. The model features closed-form formulas for its joint survival, cumulative distribution, and probability mass functions, enabling efficient computer implementation. We analyze the identifiability of the suggested model and the positive dependence structure, deriving the joint probability generating function and conditional expectations. The joint hazard rate function demonstrates considerable distributional flexibility, allowing for monotonic, bathtub, and unimodal shapes. Subsequent to the derivation of maximum likelihood estimators and the Fisher information matrix, we conduct simulation investigations across several sample sizes. The suggested model, when applied to three authentic datasets from the healthcare and manufacturing sectors, demonstrates a better fit than competitive models based on standard statistical selection criteria, confirming its efficacy for modeling count data.