A beta–epsilon distribution: properties and applications

A new probability distribution, called the beta–epsilon distribution, is introduced in this study and shown to possess desirable statistical properties for application in reliability studies. Its hazard rate function is bathtub shaped, and exhibits differing shapes with increasing value of its upper support parameter, δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}. The boundedness of the upper limit describes its potential to model finite lifetimes of systems, organisms and humans. Two real life applications in this study provided good fit to the data and further buttress the potential of the application of the new distribution.