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.

This paper introduces a novel and highly flexible two-parameter discrete distribution designed for modeling complex count data. We comprehensively derive its statistical, reliability, and actuarial properties, establishing key metrics including moments, entropy, stochastic orders, and risk measures such as value-at-risk and tail-value-at-risk. The proposed model is particularly adept at capturing right-skewed, overdispersion data characterized by outliers and varying kurtosis. Notably, its hazard rate function accommodates diverse shapes, including increasing, decreasing, unimodal, bathtub, and J-shaped, while asymptotically approaching a constant to exhibit geometric-like memoryless properties. Model parameters are estimated via the maximum likelihood method for both complete and censored datasets. Additionally, we develop computationally efficient Monte Carlo simulation strategies leveraging these versatile hazard profiles. Empirical applications across actuarial science, clinical nephrology, and agricultural entomology demonstrate the model's superior efficacy in capturing extreme values when compared to existing competing distributions.