Stochastic comparisons between extreme order statistics from scale models

Torrado, Nuria

doi:10.1080/02331888.2017.1316505

Cited by 19 publications

(3 citation statements)

References 27 publications

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“…Further, in the presence of the Archimedean copula or survival copula for the random variables, they obtained the usual stochastic order of the sample extremes. Torrado (2017) addressed the problem of stochastic comparisons of the extreme order statistics from two sets of heterogeneous scale models. The author obtained various stochastic orderings when a set of parameters majorizes another set of parameters.…”

Section: Introductionmentioning

confidence: 99%

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

Das¹,

Kayal²

2021

Preprint

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The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a 2-out-of-n system. Consider two 2-out-of-n systems with heterogeneous random lifetimes. The lifetimes are assumed to follow heterogeneous general exponentiated location-scale models. In this communication, the usual stochastic and reversed hazard rate orders between the systems' lifetimes are established under two cases. For the case of independent random lifetimes, the usual stochastic order and the reversed hazard rate order between the second-largest order statistics are obtained by using the concept of vector majorization and related orders. For the dependent case, the conditions under which the usual stochastic order between the second-largest order statistics holds are investigated. To illustrate the theoretical findings, some special cases of the exponentiated location-scale model are considered.

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Section: Introductionmentioning

confidence: 99%

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

Das¹,

Kayal²

2021

Preprint

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“…The authors also extended the result given by (1.1) to the case of the proportional hazard rate models. Recently, Torrado (2017) developed the comparison result similar to (1.1) for the multiple-outlier scale models when the random variables are independent. It is noted that almost all concerned research in this area has been developed under the assumption of statistically independent component lifetimes.…”

Section: Introductionmentioning

confidence: 99%

Ordering results of extreme order statistics from multiple-outlier scale models with dependence

Das,

Kayal

2020

Preprint

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In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables. Sufficient conditions are obtained for comparison of the largest order statistics in the sense of the usual stochastic, reversed hazard rate, star and Lorenz orders. The smallest order statistics are also compared with respect to the usual stochastic, hazard rate, star and Lorenz orders. To illustrate the theoretical establishments, some examples are provided.

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“…These are done using the concept of vector majorization and related orders. 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.…”

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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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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Stochastic comparisons between extreme order statistics from scale models

Cited by 19 publications

References 27 publications

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

Ordering results of extreme order statistics from multiple-outlier scale models with dependence

Ordering Results on Extremes of Exponentiated Location-Scale Models

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