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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.

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