Schur-concave survival functions and survival analysis
Journal of Computational and Applied Mathematics
Archimedean copulae and positive dependence
Journal of Multivariate Analysis
A concept of duality for multivariate exchangeable survival models
Fuzzy Sets and Systems
On a class of transformations of copulas and quasi-copulas
Fuzzy Sets and Systems
Tails of multivariate Archimedean copulas
Journal of Multivariate Analysis
Supermigrative semi-copulas and triangular norms
Information Sciences: an International Journal
Kendall distributions and level sets in bivariate exchangeable survival models
Information Sciences: an International Journal
New constructions of diagonal patchwork copulas
Information Sciences: an International Journal
Semi-copulas, capacities and families of level sets
Fuzzy Sets and Systems
A universal integral as common frame for choquet and Sugeno integral
IEEE Transactions on Fuzzy Systems
Aging functions and multivariate notions of nbu and ifr
Probability in the Engineering and Informational Sciences
Two classes of pseudo-triangular norms and fuzzy implications
Computers & Mathematics with Applications
General Chebyshev type inequalities for universal integral
Information Sciences: an International Journal
On the α-migrativity of multivariate semi-copulas
Information Sciences: an International Journal
Semi-uninorms and implications on a complete lattice
Fuzzy Sets and Systems
Liapunov-type inequality for universal integral
International Journal of Intelligent Systems
A generalization of universal integrals by means of level dependent capacities
Knowledge-Based Systems
Generalizations of the Chebyshev-type inequality for Choquet-like expectation
Information Sciences: an International Journal
Useful tools for non-linear systems: Several non-linear integral inequalities
Knowledge-Based Systems
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For a couple of lifetimes (X1, X2) with an exchangeable joint survival function F- attention is focused on notions of bivariate aging that can be described in terms of properties of the level curves of F-. We analyze the relations existing among those notions of bivariate aging, univariate aging, and dependence. A goal and, at the same time, a method to this purpose is to define axiomatically a correspondence among those objects; in fact, we characterize notions of univariate and bivariate aging in terms of properties of dependence. Dependence between two lifetimes will be described in terms of their survival copula. The language of copulæ turns out to be generally useful for our purposes; in particular, we shall introduce the more general notion of semicopula. It will be seen that this is a natural object for our analysis. Our definitions and subsequent results will be illustrated by considering a few remarkable cases; in particular, we find some necessary or sufficient conditions for Schur-concavity of F-, or for IFR properties of the one-dimensional marginals. The case characterized by the condition that the survival copula of (X1, X2) is Archimedean will be considered in some detail. For most of our arguments, the extension to the case of n 2 is straightforward.