Fitting a multivariate failure time distribution

A class of continuous multivariate distributions is reviewed. It is derived in a survival/reliability context, where the dependence is modeled as random effects, viz, by an unobserved covariate common to the components in a system and assumed to follow a positive stable distribution. Accounting for censored data is straightforward. The class is well fitted to proportional hazard models, and distributions of minima are simple. An important subfamily is the multivariate Weibull distributions. The theory is illustrated with an example