A New Generalization of Exponentiated Exponential Distribution using Quantile Functions

Abstract

Generalising existing probability distributions increases their appeal to researchers and expands their applicability to real-life situations by adding flexibility to the existing models. In this study, a new generalised class of the exponentiated exponential (EE) distribution is introduced, referred to as the T-Exponential Exponential{Y} or T-EE{Y} class of distributions. By utilising the quantile functions of several well-known continuous distributions in the T-EE{Y} framework, six distinct subclasses have been developed. Various statistical properties such as quantiles, mode, incomplete moments, entropy, and mean deviation have been derived for these subclasses. Additionally, four specific member models within the proposed class have been explored. The study demonstrates that the members from the T-EE{Y} class exhibit flexible shapes, including unimodal, bimodal, symmetrical, and skewed (both right and left) forms. Parameter estimation is performed using the maximum likelihood estimation method, and the effectiveness of the estimators is evaluated through a Monte Carlo simulation study. To evaluate the practical applicability of the proposed class of distributions, three real-world datasets are analysed. The members of the proposed class consistently outperform several existing distributions in modelling lifetime data, showcasing its significance and versatility.