On the skewness of extreme order statistics from heterogeneous samples

Ding, Weiyong; Yang, Jiaxin; Ling, Xiaoliang

doi:10.1080/03610926.2015.1041984

Cited by 23 publications

(15 citation statements)

References 14 publications

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“…Note that Ding et al (2017) obtained the result in Theorem 3.6 for the special case of k = n under the multiple-outlier power-generalized Weibull model, which includes the multipleoutlier Weibull model as a special case.…”

Section: Resultsmentioning

confidence: 88%

On stochastic comparisons ofk-out-of-nsystems with Weibull components

Barmalzan

Haidari

2018

J. Appl. Probab.

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In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).

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Section: Resultsmentioning

confidence: 88%

On stochastic comparisons ofk-out-of-nsystems with Weibull components

Barmalzan

Haidari

2018

J. Appl. Probab.

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“…Further, Assumption 3.5 is equivalent to saying that th F (t) is increasing in t ∈ R + , and Assumption 3.6 is equivalent to saying that tr F (t) is decreasing in t ∈ R + . These simplified conditions are fulfilled by some well-known distributions within the scale family; see Ding et al (2017); Zhang et al (2019). (b) PHR family: In this case, we haveF(t; λ) = F λ (t), t ∈ R + .…”

Section: Corollary 32: Under the Setting Of Corollarymentioning

confidence: 99%

Stochastic comparisons on total capacity of weighted k-out-of-n systems with heterogeneous components

Zhang

2021

Statistical Theory and Related Fields

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This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n systems with heterogeneous components. The expectation order, the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of system capacity. Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights. Some examples are also provided as illustrations.

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“…Specifically, they established star ordering for the proportional hazard rate model under some restrictions on parameters and presented results on Weibull and Pareto distributed samples. More recently, Ding et al [5] considered a scale model framework and examined the effect of heterogeneity on the skewness of the largest order statistics from such samples in the sense of star ordering. They proved that, without any restriction on the scale parameters, the skewness of the largest order statistics from heterogeneous samples is more than that from homogeneous samples.…”

Section: Introductionmentioning

confidence: 99%

Stochastic comparison of parallel systems with Pareto components

Naqvi¹,

Ding²,

Zhao³

2021

Prob. Eng. Inf. Sci.

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Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

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On the skewness of extreme order statistics from heterogeneous samples

Cited by 23 publications

References 14 publications

On stochastic comparisons ofk-out-of-nsystems with Weibull components

On stochastic comparisons ofk-out-of-nsystems with Weibull components

Stochastic comparisons on total capacity of weighted k-out-of-n systems with heterogeneous components

Stochastic comparison of parallel systems with Pareto components

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