On stochastic comparisons of maximum order statistics from the location-scale family of distributions

Hazra, Nil Kamal; Kuiti, Mithu Rani; Finkelstein, Maxim; Nanda, Asok K.

doi:10.1016/j.jmva.2017.06.001

Cited by 51 publications

(33 citation statements)

References 22 publications

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Order By: Relevance

“…Second part of the theorem shows similar result for the same sets of location and shape parameters. are respectively increasing and decreasing in u, then λ w μ ⇒ X n: Next result generalizes Theorem 8(iii) of Hazra et al [20]. We assume that two sets of independent random variables have the same sets of location and shape parameters, but different sets of scale parameters.…”

Section: Hazard Rate and Reversed Hazard Rate Orderssupporting

confidence: 57%

“…Torrado [40] obtained various ordering results for the comparisons of two extreme order statistics from scale models when one set of scale parameters majorizes the other. Hazra et al [20] obtained various stochastic comparisons of the maximum order statistics from the location-scale family of distributions. Recently, Hazra et al [21] considered stochastic comparisons of the minimum order statistics from the location-scale family of distributions.…”

Section: Introductionmentioning

confidence: 99%

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Ordering Results on Extremes of Exponentiated Location-Scale Models

Das¹,

Kayal²,

Choudhuri³

2019

Prob. Eng. Inf. Sci.

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In this paper, we consider exponentiated location-scale model and obtain several ordering results between extreme order statistics in various senses. Under majorization type partial order-based conditions, the comparisons are established according to the usual stochastic order, hazard rate order and reversed hazard rate order. Multiple-outlier models are considered. When the number of components are equal, the results are obtained based on the ageing faster order in terms of the hazard rate and likelihood ratio orders. For unequal number of components, we develop comparisons according to the usual stochastic order, hazard rate order, and likelihood ratio order. Numerical examples are considered to illustrate the results.

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Section: Hazard Rate and Reversed Hazard Rate Orderssupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Ordering Results on Extremes of Exponentiated Location-Scale Models

Das¹,

Kayal²,

Choudhuri³

2019

Prob. Eng. Inf. Sci.

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“…Stochastic comparisons of coherent systems are considered to be one of the important problems in reliability theory. A comprehensive list of results so far developed on various stochastic comparisons of k-out-of-n systems with independent components can be found in [3], [25], [49], [51], and the references therein. Further, stochastic comparisons of general coherent systems have been considered in [1], [6], [16], [30], [42], [43], [44], [45], [47], and [53], to name a few.…”

Section: Introductionmentioning

confidence: 99%

On relative ageing of coherent systems with dependent identically distributed components

Hazra

Misra

2020

Adv. Appl. Probab.

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Relative ageing describes how one system ages with respect to another. The ageing faster orders are used to compare the relative ageing of two systems. Here, we study ageing faster orders in the hazard and reversed hazard rates. We provide some sufficient conditions for one coherent system to dominate another with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders.

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“…Li and Fang [20] investigated the ordering properties of the extremes of dependent scaled random variables. Further, Hazra et al [21,22], adding a location parameter to a scale distribution, obtained a location-scaled distribution family and compared extreme order statistics from this distribution family. In addition, a new distribution family was obtained by adding a shape parameter α to the baseline distribution function.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components

2020

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This paper deals with stochastic comparisons of two parallel (series) systems with Type II half logistic-resilience scale (TIIHL-RS) distribution components with different baseline distribution functions. Under the conditions of interdependency and independency, the research shows that the system performance is better (worse) with the stronger component heterogeneity in the parallel (series) system under the usual stochastic order and the (reversed) hazard rate order.

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On stochastic comparisons of maximum order statistics from the location-scale family of distributions

Cited by 51 publications

References 22 publications

Ordering Results on Extremes of Exponentiated Location-Scale Models

Ordering Results on Extremes of Exponentiated Location-Scale Models

On relative ageing of coherent systems with dependent identically distributed components

Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components

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