SCHUR-CONCAVE SURVIVAL FUNCTIONS AND SURVIVAL ANALYSIS

We consider an N-tuple of exchangeable nonnegative random variables, which can, e.g., be interpreted as lifetimes of N similar units, and we assume that the joint survival function F(N)BAR(X1, ..., X(N)) = P{X1 > x...... X(N) > x(N)} is, in particular, Schur-concave. This condition is relevant since, as it has been recently shown, it provides a probabilistic model for aging in the subjectivist set-up. In this paper we analyze general properties of Schur-concave survival functions and give representation theorems. In particular, we study properties of Schur-concave survival distributions which are a finite-population version of time-transformed exponential distributions. These distribution models are of interest in analyzing life data.