On stochastic comparisons of minimum order statistics from the location–scale family of distributions

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

doi:10.1007/s00184-017-0636-x

Cited by 24 publications

(11 citation statements)

References 28 publications

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“…Hazra et al (2017) considered the problem of stochastic comparison for the largest order statistics from locationscale family of distributions. Hazra et al (2018) obtained various stochastic comparison results between minimum order statistics for general location-scale model. and respectively obtained some ordering results for the extreme order statistics arising from dependent and independent heterogeneous exponentiated location-scale (ELS) random observations.…”

Section: Introductionmentioning

confidence: 99%

On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

Das,

Kayal

2021

Preprint

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Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of parameters is switched to another vector of parameters in the specified model. Sufficient conditions for the usual stochastic order and the hazard rate order are derived. Some applications of the established results are presented.

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Section: Introductionmentioning

confidence: 99%

On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

Das,

Kayal

2021

Preprint

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“…For the location-scale distributed samples, Hazra et al (2017) obtained various stochastic ordering results between the maximum order statistics. Hazra et al (2018) considered independent heterogeneous location-scale models and obtained stochastic comparisons between the minimum order statistics in terms of various stochastic orders. Fang and Xu (2019) developed comparison results between the lifetimes of series and parallel systems with heterogeneous exponentiated gamma components.…”

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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“…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 minimum order statistics from the location–scale family of distributions

Cited by 24 publications

References 28 publications

On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

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

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

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