Applications in engineering and medicine with new generalized class of distribution: Properties, estimation methods, and simulation

A novel distribution family named the Transmuted Odd Moment Exponential-G (TOME-G) family is introduced, derived from both the Odd Moment Exponential-G and Transmuted families. Within this family, three distinct models are proposed: the transmuted odd moment exponential Lomax (TOMEL) distribution, transmuted odd moment exponential Rayleigh (TOMER) distribution, and transmuted odd moment exponential exponential (TOMEE) distribution. The density function shape for each model, such as symmetric or asymmetric (including right-skewed, left-skewed, increasing, decreasing, and uni-modal), is discussed. Key statistical characteristics of the family, including the expansion of the probability density function (PDF), moments, incomplete moment, Mo generating function, residual life, and reversed residual life functions, are derived. Additionally, three estimation methods—maximum likelihood estimation (MLE), Ordinary Least Squares Estimator (OLSE), and Weighted Least Squares Estimator (WLE)—are examined for estimating model parameters. A simulation study is conducted to compare the performance of these estimation methods. We covered two real-life applications in this study, both involving life tests. One of them is in the engineering domain, aiming to study the time to failure between manufactured units. The other application is in the medical field, focusing on leukemia data for life tests.