Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes

By Bruno Bassan, Fabio Spizzichino. 2005

179 citations recorded by the source corpus.

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 copulae 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.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/783c0ef2c6290a9788fb109c5ce1c33057f8f3df

How researchers see this paper

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In Finance

1. Fabrizio Durante
2. Peter Sarkoci
3. Rui Fang
4. Xiaohu Li
5. Chen Li
6. Endre Pap
7. Carlo Sempi
8. G. Salvadori

In Management Science and Operations Research

1. Fabrizio Durante
2. Endre Pap
3. Peter Sarkoci
4. Rui Fang
5. Xiaohu Li
6. Radko Mesiar
7. Chen Li
8. G. Salvadori

In Statistics and Probability

1. Rui Fang
2. Chen Li
3. Xiaohu Li
4. Endre Pap
5. Radko Mesiar
6. Fabrizio Durante
7. G. Salvadori

Citations in the corpus

• Stochastic comparisons on sample extremes of dependent and heterogenous observations (2016, methodology): “For more details on log-convexity and log-concavity of generators of Archimedean copulas, one may refer to Bassan and Spizzichino [27] and Müller and Scarsini.”
• Copula Theory: An Introduction (2010, unknown): “ory, this kind of transformation is used in order to introduce the so-called bivariate ageing function that are used for the definition of bivariate notion of ageing (see [8, 9, 53, 148]).”
• Distorted Copulas: Constructions and Tail Dependence (2010, background): “Thus they are (continuous) semi-copulas, but not necessarily copulas (see Bassan and Spizzichino (2001, 2005b) ; Durante and Sempi (2005a,b)).”
• A Universal Integral as Common Frame for Choquet and Sugeno Integral (2010, background): “Recall that a semicopula (conjunctor, t-seminorm) [3], [12], [63] is a binary operation⊗ : [0, 1]2 → [0, 1] that is nondecreasing in both components, has 1 as neutral element and satisfies a ⊗ b ≤ min(a, b) for all (a, b) ∈ [0, 1]2 .”