A Mixture Model of Two Bivariate Weibull Distributions

Abstract

In this paper, we propose a mixture model containing bivariate Weibull distributions—theMarshall-Olkin bivariate Weibull (MOBW) and the Block-Basu bivariate Weibull (BBBW)—because each of these distributions alone is inadequate for explaining a data set when certainspecial situations occur in bivariate lifetime data sets. We refer to the proposed model asMix_BW. To estimate the model parameters, we use the expectation-maximisation (EM)algorithm in an adapted form we term the Mix_EM algorithm. We provide illustrative exampleswith real and simulated data sets to demonstrate the applicability of the proposed Mix_BWmodel.