A Flexible Alpha Power Exponentiated Family of Distributions for Regression and Lifetime Data Modeling

Developing flexible probability distributions capable of capturing complex features observed in lifetime data remains a fundamental challenge in statistical modeling. The limitations of classical probability distributions in adequately modeling varying degrees of skewness, heavy-tailed behavior, and nonmonotonic failure rates have motivated the development of more flexible distributional families based on diverse transformation mechanisms. This paper introduces the alpha power new exponentiated family (APNEF) of distributions, a unified framework that integrates two transformation mechanisms: the new exponentiation transformation and the alpha power transformation. The proposed family extends baseline distributions through multiple shape parameters, enabling flexibility in capturing complex data structures while maintaining computational tractability. We derive key statistical properties of the APNEF, including the quantile function, noncentral and incomplete moments, the Rényi entropy, and the Lorenz and Bonferroni inequality curves. A suite of estimation procedures is developed and assessed via Monte Carlo simulation, evaluating finite-sample performance and consistency and offering guidance on estimator choice. We extend the APNEF to a log-location-scale regression framework to facilitate its application in regression settings. The resulting model falls within the accelerated failure time class, with covariates entering linearly on the log-response scale and a shape parameter determining the form of the error term. The theoretical and empirical effectiveness of the proposed family is demonstrated through applications to lifetime datasets, where the alpha power new Weibull distribution, a member of the APNEF family, consistently outperforms numerous competing models. The findings establish APNEF as a valuable and flexible framework for statistical inference in reliability analysis, survival studies, and other applied domains.