Bivariate inverse Weibull distribution

Abstract

Recently it is observed that the inverse Weibull (IW) distribution can be used quite effectively to analyse lifetime data in one dimension. The main aim of this paper is to define a bivariate inverse Weibull (BIW) distribution so that the marginals have IW distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in compact forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. We obtained the maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance– covariance matrix. We perform some simulations to see the performances of the maximum likelihood estimators. One data set has been re-analysed and it is observed that the bivariate IW distribution provides a better fit than the bivariate exponential distribution.