A discrete extension of the exponential type II distribution: statistical characterizations, reliability analysis, and Bayesian vs. non-Bayesian inferences for random right-censored and complete count data

This study focuses on applying a discrete distribution designed to effectively model both complete and censored data. The proposed distribution serves as a discrete analogue of the binomial exponential type II distribution. In contrast to many well-established discrete models in the literature, this distribution presents tractable, closed-form expressions, revealing distinctive structural properties not previously addressed. This paper explores key reliability properties through the analysis of various systems, recurrence relation for probabilities, long-tailedness, entropies, and order statistics, along with their associated L-moments. By thoroughly examining its structural characteristics, we demonstrate that this distribution possesses an increasing failure rate function, making it particularly suitable for modeling over- or under-dispersed data. Estimation of the unknown parameters in both complete and censored data scenarios is performed using classical and Bayesian methodologies. Furthermore, an algorithm for generating random right-censored data from the proposed model is elucidated. To validate the performance of the estimators, two extensive simulation studies are conducted, scrutinizing their behavior in the presence of complete and random right-censored data. Finally, the practical utility of the distribution is demonstrated by applying it to four real datasets, including two complete datasets and two censored datasets. These empirical applications demonstrate the model’s flexibility in addressing a broad spectrum of practical scenarios.