A Novel Generalization of the Inverted Nadarajah–Haghighi Distribution with Estimation Methods and Medical Applications

Abstract

Statisticians and data analysts often use statistical probability distributions to describe and analyze their data. However, traditional distributions may not always accommodate certain data sets, making it necessary to develop new models to handle complex data structures and improve fit quality. This paper introduces a new extended lifetime model, called the New Exponential Inverted Nadarajah–Haghighi distribution (NEINH), which belongs to the new exponential-X family of distributions. This approach is designed to model complex data in a variety of applications. The article explores some of the statistical properties of this proposed distribution such as quantile function, moment, moment generating function, order statistic and others. The NEINH's parameters are estimated using the Bayesian estimation method, maximum likelihood method, and five other methods. The efficacy of this distribution is established by its comparative analysis with alternative distributions, using four real-world medical datasets to highlight its superior performance.