A Novel Probability Distribution with Robust Parametric Properties

Abstract

The continuous evolution of statistical modelling has spurred the development of novel probability distributions to address complex data challenges. This paper introduces the Topp-Leone Epsilon (TopLE) distribution, derived by combining the Topp-Leone and epsilon distributions. The TopLE distribution exhibits attractive parametric properties, including flexible shape and scale parameters, a closed-form quantile function, and efficient parameter estimation using computational tools. Simulation studies demonstrate the distribution's efficiency, consistency, and stability, making it suitable for a wide range of applications in lifetime data analysis. Two comparative applications with four standard distributions have shown the TopLE distribution to be a competitive choice in modelling real-life datasets. This work contributes to the statistical literature by providing a versatile and competitive model for modern data complexities.