On record-based transmuted X-lindley distribution: Properties and applications

In this paper, a novel record-based transmuted version of the X-Lindley distribution is introduced, and dubbed as the record-based transmuted X-Lindley (RTXL) distribution. The analysis describes several statistical features of the proposed distribution such as moments, stochastic ordering, quantiles and order statistics. Additionally, the reliability features such as the reliability function, hazard rate function, reverse hazard rate function and mean residual life function are thoroughly analyzed. Parameters of the RTXL distribution are estimated using the maximum likelihood method, and a simulation study confirms the efficiency and asymptotic performance of these estimators. The practical utility of the RTXL distribution is demonstrated through real-world data sets, where it consistently provides a superior fit compared to competing models. These results highlight both the theoretical contribution and the practical value of the RTXL distribution. In addition to biomedical and service applications, the model shows strong potential for industrial reliability and predictive maintenance, aligning with the objectives of Industry 4.0 and smart manufacturing. Future research directions include extensions to censored data, Bayesian inference, regression modeling, and multivariate generalizations.