463 research outputs found
Revisiting Relations between Stochastic Ageing and Dependence for Exchangeable Lifetimes with an Extension for the IFRA/DFRA Property
We first review an approach that had been developed in the past years to
introduce concepts of "bivariate ageing" for exchangeable lifetimes and to
analyze mutual relations among stochastic dependence, univariate ageing, and
bivariate ageing. A specific feature of such an approach dwells on the concept
of semi-copula and in the extension, from copulas to semi-copulas, of
properties of stochastic dependence. In this perspective, we aim to discuss
some intricate aspects of conceptual character and to provide the readers with
pertinent remarks from a Bayesian Statistics standpoint. In particular we will
discuss the role of extensions of dependence properties. "Archimedean" models
have an important role in the present framework. In the second part of the
paper, the definitions of Kendall distribution and of Kendall equivalence
classes will be extended to semi-copulas and related properties will be
analyzed. On such a basis, we will consider the notion of "Pseudo-Archimedean"
models and extend to them the analysis of the relations between the ageing
notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD
Relations Between Stochastic Orderings and generalized Stochastic Precedence
The concept of "stochastic precedence" between two real-valued random
variables has often emerged in different applied frameworks. In this paper we
consider a slightly more general, and completely natural, concept of stochastic
precedence and analyze its relations with the notions of stochastic ordering.
Such a study leads us to introducing some special classes of bivariate copulas.
Motivations for our study can arise from different fields. In particular we
consider the frame of Target-Based Approach in decisions under risk. This
approach has been mainly developed under the assumption of stochastic
independence between "Prospects" and "Targets". Our analysis concerns the case
of stochastic dependence.Comment: 13 pages, 6 figure
Generalized Marshall-Olkin Distributions, and Related Bivariate Aging Properties
National Natural Science Foundation of China [10771090]A class of generalized bivariate Marshall-Olkin distributions, which includes as special cases the Marshall-Olkin bivariate exponential distribution and the Marshall-Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with properties related to evolution of dependence along time, are investigated for this class of distributions. Extensions of results previously presented in the literature are provided as well. (C) 2011 Elsevier Inc. All rights reserved
Copulas in Hilbert spaces
In this article, the concept of copulas is generalised to infinite
dimensional Hilbert spaces. We show one direction of Sklar's theorem and
explain that the other direction fails in infinite dimensional Hilbert spaces.
We derive a necessary and sufficient condition which allows to state this
direction of Sklar's theorem in Hilbert spaces. We consider copulas with
densities and specifically construct copulas in a Hilbert space by a family of
pairwise copulas with densities
Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes
As a motivating problem, we aim to study some special aspects of the marginal
distributions of the order statistics for exchangeable and (more generally) for
minimally stable non-negative random variables . In any case,
we assume that are identically distributed, with a common
survival function and their survival copula is denoted by .
The diagonal's and subdiagonals' sections of , along with ,
are possible tools to describe the information needed to recover the laws of
order statistics.
When attention is restricted to the absolutely continuous case, such a joint
distribution can be described in terms of the associated multivariate
conditional hazard rate (m.c.h.r.) functions. We then study the distributions
of the order statistics of also in terms of the system of the
m.c.h.r. functions. We compare and, in a sense, we combine the two different
approaches in order to obtain different detailed formulas and to analyze some
probabilistic aspects for the distributions of interest. This study also leads
us to compare the two cases of exchangeable and minimally stable variables both
in terms of copulas and of m.c.h.r. functions. The paper concludes with the
analysis of two remarkable special cases of stochastic dependence, namely
Archimedean copulas and load sharing models. This analysis will allow us to
provide some illustrative examples, and some discussion about peculiar aspects
of our results
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