A new useful three-parameter extension of the exponential distribution

Abstract

A three-parameter extension of the exponential distribution is introduced and studied in this paper. The new distribution is quite flexible and can be used effectively in modelling survival data, reliability problems, fatigue life studies and hydrological data. It can have constant, decreasing, increasing, upside-down bathtub (unimodal), bathtub-shaped and decreasing–increasing–decreasing hazard rate functions. We provide a comprehensive account of the mathematical properties of the new distribution and various structural quantities are derived. We discuss maximum likelihood estimation of the model parameters for complete sample and for censored sample. An empirical application of the new model to real data is presented for illustrative purposes. We hope that the new distribution will serve as an alternative model to other models available in the literature for modelling real data in many areas.

Keywords:

• censored data
• exponential distribution
• lifetime data
• Marshall–Olkin extended distribution
• maximum likelihood estimation

Acknowledgments

We are very grateful to the associate editor and two anonymous referees for valuable comments and suggestions which have improved considerably the first version of the manuscript. Artur Lemonte and Gauss Cordeiro gratefully acknowledge financial support from CNPq (Brazil) and FACEPE (Pernambuco, Brazil), and Germán Moreno–Arenas gratefully acknowledges grants from Mobility Program of the Universidad Industrial de Santander (Bucaramanga, Colombia).

Disclosure

No potential conflict of interest was reported by the authors.