A Transformation for the Analysis of Unimodal Hazard Rate Lifetimes Data

Abstract

The family of distributions introduced by [34] is the best known, best understood, most extensively investigated, and commonly employed model used for lifetimes data analysis. A variety of software packages are available to simplify its use. Yet, as is well known, the model is appropriate only when the hazard rate is monotone. However, as suggested in an overview by [23], the software packages may be usefully employed by transforming data when exploratory tools such as TTT transform or nonparametric estimates indicate unimodal, bathtub or J-shaped hazard rates, which are also commonly encountered in practice. Mudholkar et al. [22] discussed the details of one such transformation relevant for the bathtub case. In this paper, specifics of another transformation which is appropriate when data exploration indicates a unimodal hazard rate is discussed. The details of parameter estimation and hypothesis testing are considered in conjunction with earlier alternatives and illustrated using examples from the fields of biological extremes and finance.