In this work we present the Power Variance Function (PVF) copula family to model the dependence structure of multivariate lifetime data.

The PVF copula family includes the Clayton, Positive Stable (Gumbel) and Inverse Gaussian copulas as special or limiting cases.

Dependence properties of the copula models are explored and described. We adapt a new general simulation technique to simulate from the PVF copula.

We suggest a Bayesian approach to parameter estimation of the PVF copula using MCMC for posterior computation. A simulation study is performed to investigate the small sample properties of the estimates.

Finally, we illustrate the usefulness of the methodology using data from the Australian NH&MRC Twin registry. Parameters of the marginal distributions

and the PVF copula are simultaneously estimated where the marginal distributions are modelled using Weibull and piecewise exponential distributions.