A New Generalization of Double XRamma Distribution: Statistical Properties and Applications to Real Data

In this article, we introduce and study a new extension of the double XRamma distribution, referred to as the power double XRamma distribution (PDXRD), by employing a power transformation strategy. The proposed PDXRD provides increased flexibility over the baseline distribution and is capable of accommodating a broader range of real-world data. The PDXRD possesses several attractive structural properties, including a flexible decrease, a unimodal shape, close to symmetry, and a right-skewed probability density function (PDF), as well as a versatile hazard rate function (HRF) that can exhibit either increasing or decreasing behavior. Several important mathematical and statistical properties are computed, covering ordinary and incomplete moments, mean, variance, skewness, kurtosis, coefficient of variation, moment generating function, conditional moments, mean residual life, Lorenz curve, mean past lifetime, extropy measures, and order statistics. The unknown two parameters of the PDXRD are estimated utilizing the maximum likelihood method, and the corresponding point and interval estimates are assessed through an extensive simulation study. Finally, the practical performance and importance of the proposed PDXRD are illustrated using two real-world datasets related to engineering and survival times data. The numerical results demonstrate that the PDXRD provides a superior fit compared with several well-known competing statistical distributions, highlighting its potential as an effective and flexible model for analyzing complex data arising in diverse applied fields such as engineering and survival times.