A Bivariate Weibull Distribution and Its Applications in Reliability

In this article, the bivariate exponential distribution proposed by Downton (“Bivariate exponential distributions in reliability theory”, Journal of the Royal Statistical Society Series B, 1970) is extended to a bivariate Weibull distribution, and it is called the Downton’s bivariate Weibull (DBW) distribution. Statistical properties of the DBW distribution are explored and likelihood inference developed based on complete as well as right-censored bivariate data are discussed. Through extensive Monte Carlo simulations, performance of the point and interval estimates are evaluated. Two real datasets are analyzed for illustrative purposes. It is concluded that the DBW distribution is very useful to model bivariate data.