New Lindley Generator Based on T-X Family of Distributions: Properties and Reliability Applications

The generalization of probability distributions has a rich history, with various techniques employed to introduce new families of distributions. One notable approach is the transformed-transformer (T-X) method, which has been used by several authors to introduce many of novel probability distributions. In this study, we present the new Lindley-X class, a novel family of continuous probability distributions, and we introduce some submodels within this framework. Our research involves deriving mathematical expressions for various statistical measures, including moments, the generating function, the quantile function, and Renyi entropy. To estimate the parameters of the new family of distributions, we utilize a range of methods, including maximum likelihood, maximum product spacing, least squares, Cramer-von Mises, and Anderson-Darling estimations. Furthermore, we illustrate the practical applicability of this new family of distributions through the analysis of real-life datasets.