Modeling of Time-to-Event Data Using a New Alpha Power Logarithmic Class of Lifetime Distributions

This article introduces a new family of lifetime distributions, termed the alpha power logarithmic transformed family (APLo-F), and investigates its genesis and key distributional characteristics. A particular member of this family, the alpha power logarithmic transformed exponential (APLo-E) distribution, is derived by applying the proposed transformation to the one-parameter exponential distribution. The structural behavior of the APLo-E distribution is examined in detail, and mathematical conditions governing its hazard rate function (HRF) are established. A comprehensive analytical study is carried out to derive several statistical properties, including moments, conditional moments, generating functions, entropies, mean deviation, order statistics, and inequality measures such as the Bonferroni and Lorenz curves. The parameters of the proposed model are estimated using the well-known maximum likelihood estimation (MLE) technique, and the reliability and hazard functions are further estimated through the invariance property of MLE. A Monte Carlo simulation study is performed to assess the consistency and efficiency of the estimators. Finally, the practical applicability of the proposed distribution is illustrated using reliability and survival dataset from diverse application domains. The results demonstrate the flexibility, reliability, and superior performance of the APLo-E distribution in modeling time-to-event data. Overall, this study contributes a novel class of lifetime distributions and provides robust theoretical and practical tools for analyzing reliability and survival phenomena.