Bivariate extension of bathtub-shaped distribution

Abstract

Modeling of bathtub-shaped hazard rate function commonly arises in reliability and survival analyses. The present article introduces a bivariate extension of the Chen distribution that has bathtub-shaped hazard function. The proposed distribution has closed-form expressions for the joint survival function and conditional distributions. Several properties of the proposed distribution such as joint moments, marginals and conditional distributions are discussed. We obtain maximum likelihood estimators for estimating the unknown parameters using the expectation-maximization algorithm. At the end, application of the proposed distribution is illustrated by means of a real-life application. © 2022, The Author(s), under exclusive licence to Society for Reliability and Safety (SRESA).