Comprehensive Characterizations, Information Measures, and Reliability Applications for the Yun–Linear Exponential Lifetime Model

We propose the three-parameter Yun–Linear Exponential (YLE) distribution, with a specific focus on its comprehensive characterizations based on truncated moments, hazard functions, and conditional expectations. In addition, a hazard-based characterization is empirically illustrated through a diagnostic plot that compares the theoretical characterization function with its empirical counterpart, providing further support for the proposed model. To provide a comprehensive analysis of the model’s information content, we evaluate a collection of information measures, including Rényi entropy, Tsallis entropy, extropy, and cumulative residual entropy, alongside fundamental statistical properties, such as ordinary moments, generating function, and quantile function. Model parameters are estimated using the maximum-likelihood method, with their performance and finite-sample properties validated through extensive Monte Carlo simulation studies. Finally, the practical utility of the YLE model is demonstrated through two distinct reliability applications, analyzing MRI scanner failure times and repairable item intervals, confirming its robustness and flexibility in modeling heavily skewed lifetime data.