Development and characterization of a flexible three-parameter lifetime distribution: theoretical properties and real-world applications

Abstract In this article, we propose a new three-parameter lifetime distribution and derive some of its properties. This new distribution is suitable for analyzing failure time data with decreasing or unimodal-shaped hazard rates. Although the moment generating function of the distribution does not exist in closed-form, all moments exist and have closed-form expressions. The nice expressions for its density function, distribution function, hazard function, and quantile function make the distribution attractive to researchers in reliability and life testing experiments. Various structural properties, including moment generating function, mean deviations, entropy measures, tail behavior, and density-quantile function, are studied. The distribution can be classified as short- or long-tailed based on the density-quantile function. We first consider maximum likelihood and Bayesian methods of estimation for complete samples and study two different real-life applications. Then, we consider the maximum likelihood and Bayesian methods for censored samples with and without cure fraction, with and without covariates, and study one real-life application in this scenario.