A multivariate mixture of Weibull distributions in reliability modeling

A new class of multivariate distribution is derived where each component is a mixture of Weibull distribution. The approach in this paper is based on the introduction of an exponentially distributed latent random variable. The new class includes several multivariate and bivariate models including Marshall and Olkin type. The moment generating function and, hence, the correlation structure is obtained for the bivariate situation. The distribution of the minimum in a competing risk framework is discussed and various other properties including correlation structures are investigated.