Negative dependence in the balls and bins experiment with applications to order statistics

Hu, Taizhong; Xie, Chaode

doi:10.1016/j.jmva.2005.09.008

Cited by 13 publications

(12 citation statements)

References 17 publications

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“…From the fact that P(X j:n > t + t 1 |X i:n = t 1 ) is decreasing in i, see Hu and Xie (2006), and the assumption that s j|i is decreasing in i,H i,t 1 (t + t 1 ) is decreasing in i. If p(t 1 ) = ( p 1 (t 1 ), .…”

Section: Corollary 3 Under Assumptions Of Theorem 5mentioning

confidence: 97%

On the stochastic and dependence properties of the three-state systems

Ashrafi

Asadi

2014

Metrika

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Suppose that a system has three states up, partial performance and down. We assume that for a random time T 1 the system is in state up, then it moves to state partial performance for time T 2 and then the system fails and goes to state down. We also denote the lifetime of the system by T , which is clearly T = T 1 + T 2 . In this paper, several stochastic comparisons are made between T , T 1 and T 2 and their reliability properties are also investigated. We prove, among other results, that different concepts of dependence between the elements of the signatures (which are structural properties of the system) are preserved by the lifetimes of the states of the system (which are aging properties of the system). Various illustrative examples are provided.

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Section: Corollary 3 Under Assumptions Of Theorem 5mentioning

confidence: 97%

On the stochastic and dependence properties of the three-state systems

Ashrafi

Asadi

2014

Metrika

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“…. , X n:n ) given X i:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006). …”

mentioning

confidence: 65%

A Note on Conditioning and Stochastic Domination for Order Statistics

Dubhashi

Häggström

2008

J. Appl. Probab.

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“…Proof of Proposition 17 We have seen that X SP Y if and only if Q(X, Y ) − Q(Y, X) ≥ 0. Then, substituting the values of the relations, we obtain that X SP Y if and only if Q(X, Y ) − Q(Y, X) ≥ 0, that is equivalent to:…”

Section: Appendix Proofs and Technical Resultsmentioning

confidence: 93%

“…When the alternatives are defined under randomness, they are usually modeled by means of random variables. The comparison of random variables is a longstanding problem that has been tackled from many points of view (see among others [2,17,26,27]). …”

Section: Introductionmentioning

confidence: 99%

Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fr e ´ chet–Hoeffding upper bound

Montes

2016

Journal of Multivariate Analysis

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Please cite this article as: I. Montes, S. Montes, Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fréchet-Hoeffding upper bound, Journal of Multivariate Analysis (2015), http://dx. AbstractStochastic dominance and statistical preference are stochastic orders with different interpretations: the former is based on the comparison of the marginal distributions while the latter is based on the joint distribution. Sklar's Theorem allows expressing the joint distribution in terms of the marginals by means of a copula. This paper investigates the relationship between these two stochastic orders for comonotone random variables and random variables coupled by an Archimedean copula.

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Negative dependence in the balls and bins experiment with applications to order statistics

Abstract: Dependence properties of occupancy numbers in the balls and bins experiment are studied. Applying such properties, we investigate further dependence structures of order statistics X

Cited by 13 publications

References 17 publications

On the stochastic and dependence properties of the three-state systems

On the stochastic and dependence properties of the three-state systems

A Note on Conditioning and Stochastic Domination for Order Statistics

Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fr e ´ chet–Hoeffding upper bound

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