The Transformed Transmuted-G Distribution: A New Class of Exponential Generators

Data arising from diverse real-world processes often exhibit heterogeneous distributional characteristics ranging from skewness, heavy or light tails, kurtosis, presence of outliers and complex-shaped hazard rate behavior, mainly caused by the intricate pattern-generating variables in the dataset. In the past decade, considerable attention has been devoted to modelling such multifaceted behavior outside conventional distributions through developing flexible probability distributions through mixtures, convolutions, introduction of extra parameters and CDF generators. CDF-based generator families have become important tools for constructing flexible PDFs from well-known baseline distributions by addition of shape parameters potentially influencing flexibility of the probability models. Advanced CDF generators include beta-generated distributions, Kumaraswamy, Marshall-Olkin, Transmuted families, Generalized Weibull, Zubair, and Alpha-powered families. Despite this significant progress, available CDF generators do not model multiple characteristics simultaneously, potentially leading to information loss, hence the need for alternative CDF generators. This paper introduces a new CDF generator called the Transformed Transmuted Weibull-G and develops two distributions: Transformed Transmuted Exponential and Transformed Transmuted Weibull. The proposed generator exhibits substantially flexible density functions and hazard rate functions capable of modelling increasing, decreasing, unimodality, bathtub and reverse bathtub behavior from data possessing extremities of peakedness and varied tail behavior. This is clearly demonstrated through graphical and simulation studies. The statistical properties of the proposed family are derived, including quantiles, moments and order statistics. The method of maximum likelihood is used for parameter estimation, and the performance of the proposed distribution is evaluated using established goodness-of-fit criteria. The application to two sets of real data demonstrates the ability of the proposed model to provide a competitive model against selected existing distributions. The flexibility of this model makes it a highly probable candidate for application in reliability studies.