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Schur-concave survival functions and survival analysis. (English) Zbl 0773.62066
Summary: 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 \[ \overline F_ N(x_ 1,\dots,x_ N)=P\{X_ 1>x_ 1,\dots,X_ N>x_ N\} \] 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. 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.

MSC:
62N05 Reliability and life testing
62E10 Characterization and structure theory of statistical distributions
60G09 Exchangeability for stochastic processes
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