In real-life data, count data are considered more significant in different fields. In this article, a new form of the one-parameter discrete linear-exponential distribution is derived based on the survival function as a discretization technique. An extensive study of this distribution is conducted under its new form, including characteristic functions and statistical properties. It is shown that this distribution is appropriate for modeling over-dispersed count data. Moreover, its probability mass function is right-skewed with different shapes. The unknown model parameter is estimated using the maximum likelihood method, with more attention given to Bayesian estimation methods. The Bayesian estimator is computed based on three different loss functions: a square error loss function, a linear exponential loss function, and a generalized entropy loss function. The simulation study is implemented to examine the distribution’s behavior and compare the classical and Bayesian estimation methods, which indicated that the Bayesian method under the generalized entropy loss function with positive weight is the best for all sample sizes with the minimum mean squared errors. Finally, the discrete linear-exponential distribution proves its efficiency in fitting discrete physical and medical lifetime count data in real-life against other related distributions.

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.