Multivariate hazard rates and stochastic ordering

Shaked, Moshe; Shanthikumar, J. George

doi:10.2307/1427376

Cited by 37 publications

(11 citation statements)

References 19 publications

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“…It is well known that (5) implies the inequality~in (2) (see, e.g., Barlow and Proschan (1975». We note that this proposition has been extended for a more general model by Shaked and Shanthikumar (1987). However, following an idea of Schechner (1984), we are going to present a quite simple proof of (5) which points out why the symmetry displayed in (2) between the cases~(n) non-increasing and~(n) non-decreasing seems to be only partial, the dependence (positive) being very strong when~(n) is non-increasing.…”

Section: A Risk-sharing Non-linear Death Processmentioning

confidence: 71%

Interparticle dependence in a linear death process subjected to a random environment

Lefèvre

Michaletzky

1990

Journal of Applied Probability

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Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

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Section: A Risk-sharing Non-linear Death Processmentioning

confidence: 71%

Interparticle dependence in a linear death process subjected to a random environment

Lefèvre

Michaletzky

1990

Journal of Applied Probability

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“…These orders are motivated from a time-dynamic point of view and for the definitions and properties the reader can refer to [16][17][18][19]13].…”

Section: Previous Notions and Results On Stochastic Orders And Relatementioning

confidence: 99%

“…We consider the time-dynamic definition of the multivariate hazard rate order introduced by Shaked and Shanthikumar [16]. For some other extensions, from a mathematical point of view, see [20].…”

Section: Previous Notions and Results On Stochastic Orders And Relatementioning

confidence: 99%

Stochastic comparisons of multivariate mixture models

Belzunce

Mercader

Ruiz

et al. 2009

Journal of Multivariate Analysis

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Likelihood ratio Hazard rate and mean residual life orders Multivariate mixture models a b s t r a c tIn this paper we consider sufficient conditions in order to stochastically compare random vectors of multivariate mixture models. In particular we consider stochastic and convex orders, the likelihood ratio order, and the hazard rate and mean residual life dynamic orders. Applications to proportional hazard models and mixture models in risk theory are also given.

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“…Some basic properties of these functions are stated and discussed in that section. Also, the relation of these functions to the multivariate conditional hazard rate functions (discussed in Shaked and Shanthikumar (1987 » is highlighted.…”

Section: Introductionmentioning

confidence: 99%

Dynamic multivariate mean residual life functions

Shaked

Shanthikumar

1991

Journal of Applied Probability

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In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied.A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given.Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

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Multivariate hazard rates and stochastic ordering

Cited by 37 publications

References 19 publications

Interparticle dependence in a linear death process subjected to a random environment

Interparticle dependence in a linear death process subjected to a random environment

Stochastic comparisons of multivariate mixture models

Dynamic multivariate mean residual life functions

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