Applications of the Mellin Transform in Analyzing Survival Data With the Cubic Transmuted Class

The development of new models aims to provide probability distributions that can accurately describe unusual phenomena, such as those observed in survival analysis, which often pose challenges due to factors like time dependence and data censoring. Among the diverse classes and models available in the literature, there has been growing interest in transmuted distributions, particularly the cubic transmuted (CT) family, which offers enhanced flexibility for modeling complex data. Despite their advantages, these newer models lack sufficient tools to assess their goodness-of-fit adequately. To address this limitation, we apply the methodology introduced by Nicolas (2002), based on the Mellin transform (MT), to propose new goodness-of-fit measures for the CT class. We derive expressions for the MT and the log-cumulants of the CT-Weibull, CT-Log-logistic, and CT-Fréchet models. Additionally, we develop two- and three-dimensional log-cumulant diagrams as visual aids for model selection and propose a test statistic combining Hotelling’s T2 statistic with the multivariate delta method to test hypotheses about the log-cumulants. To illustrate the utility of these tools, we apply them to survival analysis data.