A Beta-New XLindley Lifetime Model with Applications

Lifetime data arise in reliability engineering, medical studies, and biological sciences, where flexible probability models are required to describe skewed and positive observations. Classical lifetime distributions are often too restrictive and may fail to capture diverse hazard rate behaviors observed in practice. In this paper, we introduce a new three-parameter lifetime model constructed by applying the beta-generated mechanism to the polynomial exponential distribution. The proposed beta—new XLindley distribution extends the baseline family by incorporating additional shape parameters that enhance modeling flexibility. Several fundamental properties of the new model are derived, including the probability density function, cumulative distribution function, reliability function, and hazard rate function. Parameter estimation is carried out using the maximum likelihood method, and numerical optimization techniques are employed to obtain the estimators. The practical performance of the proposed distribution is illustrated using a real data set consisting of luteinizing hormone measurements. Model adequacy is assessed through standard information criteria such as AIC, BIC, AICC, and the log-likelihood. The results demonstrate that the beta-new XLindley distribution provides a better fit than several well-known competing lifetime models. Overall, the proposed distribution offers a flexible and effective tool for modeling positive lifetime data and is particularly suitable for applications in medical statistics and reliability analysis.