Interactive expert assignment of minimally-informative copulae

It is increasingly recognized that good reliability practice requires giving attention to the specification of joint distributions for failure times. If the marginal distributions are known then the problem of selecting a marginal distribution is equivalent to that of selecting a copula. In the competing risk situation, identification of the copula alone is important, for together with competing risk data it enables identification of the full joint distribution. In a number of papers with various co-authors, we have suggested using the minimally informative copula with given rank correlation. In this paper a method is described of assessing minimally informative copulae using observable quantities, which gives expert guidance on the ranges allowed for coherence. This is based on using a D1AD2 algorithm instead of the DAD algorithm used to determine copulae with given rank correlation. 1 Building subjective multivariate distributions There is a growing literature on building multivariate distributions, see for example (Joe, 1997). We are particularly interested in building models with fixed marginals.