An Inferential Study of Discrete One-Parameter Linear Exponential Distribution Under Randomly Right-Censored Data

Counting data play a critical role in various real-life applications across different scientific fields. This study handles the classical and Bayesian estimation of the one-parameter discrete linear exponential distribution under randomly right-censored data. Maximum likelihood estimators, both point and interval, are derived for the unknown parameter. In addition, Bayesian estimators are gained using informative and non-informative priors, assessed under three distinct loss functions: squared error loss, linear exponential loss, and generalized entropy loss. An algorithm for generating randomly right-censored data from the proposed model is also developed. To evaluate the efficiency of the estimators, considerable simulation studies are conducted, revealing that the maximum likelihood and the Bayesian approach under the generalized entropy loss function with a positive weight consistently outperform other methods across all sample sizes, achieving the lowest root mean squared errors. Finally, the discrete linear exponential distribution demonstrates strong applicability in modeling discrete count lifetime data in physical and medical sciences, outperforming related alternative distributions.