Nonparametric priors for vectors of survival functions

The paper proposes a new nonparametric prior for two-dimensional vectors of survival functions (S1, S2). The definition is based on the Lévy copula and it is used to model, in a nonparametric Bayesian framework, two-sample survival data. Such an application yields a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We then obtain a description of the posterior distribution of (S1, S2), conditionally on possibly right-censored data. As a by-product, we find that the marginal distribution of a pair of observations from the two samples coincides with the Marshall-Olkin or the Weibull distribution according to specific choices of the marginal Lévy measures.