The generalized discrete Burr–Hatke exponential distribution: Mathematical characterization, reliability analysis, and applications to censored actuarial, clinical, and agricultural 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.