Development of a new exponential generalized family of distribution with its properties and application

Abstract

In the field of reliability analysis, the selection of an appropriate lifespan model is critical. With a multitude of lifetime distributions accessible, the hunt for a more suited distribution remains essential. In this paper, we offer a unique class of distributions derived from the notion of exponential generalization, improved with changes to boost flexibility. Our suggested distribution incorporates multiple hazard rate profiles, giving enhanced flexibility. Analytical characteristics including the rth moment, moment generating function, quantile function, distribution of order statistics, and Rényi entropy are obtained. Employing maximum likelihood estimation, we estimate the unknown parameters. Through simulation tests and analysis of real-world datasets, we exhibit the model's usefulness compared to five existing lifespan distributions, emphasising the better performance of the GAYUF distribution. This research underlines the GAYUF distribution as a better model in the field of lifespan analysis