On extreme order statistics from heterogeneous beta distributions with applications

Zhao, Peng; Wang, Lei; Zhang, Yiying

doi:10.1080/03610926.2016.1143007

Cited by 10 publications

(4 citation statements)

References 26 publications

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“…Note that the result in Theorem 3.5 contains the case when λ = 1, from which we have the following corollary for the PRHR model, which extends the above results of [36] in the context that the super-majorization in (3.14) is relaxed to…”

Section: Remark 31 It Is Worthwhile To Note Thatsupporting

confidence: 55%

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Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

Bashkar¹,

Torabi²,

Roozegar³

2017

JSTA

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The effect of heterogeneity on order statistics has attracted much attention in recent decades. In this paper, first, we discuss stochastic comparisons of extreme order statistics from independent heterogeneous exponentiated scale samples. These comparisons are made with respect to usual stochastic, reversed hazard rate and likelihood ratio orderings. Then, in the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes. In addition, some examples and applications are illustrated.

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Section: Remark 31 It Is Worthwhile To Note Thatsupporting

confidence: 55%

“…The following corollary, due to [36], provides some sufficient conditions for comparing the largest order statistics from two heterogeneous PRHR samples. Corollary 3.2.…”

Section: Remark 31 It Is Worthwhile To Note Thatmentioning

confidence: 99%

Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

Bashkar¹,

Torabi²,

Roozegar³

2017

JSTA

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“…Motivated by these, various authors have considered problems of stochastic comparisons of the lifetimes of parallel and series systems when their components are comprising of independent and heterogeneous distributions. Few recent references in this direction are [5,12,36,44]. However, there have been recent interest on studying stochastic comparisons of extreme order statistics for various general statistical models.…”

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 of parallel and series systems have been widely studied for various lifetime distributions. One may refer to other works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the references contained therein.…”

Section: Introductionmentioning

confidence: 99%

Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components

Nanda

Kayal

2018

Appl Stoch Models Bus & Ind

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In this paper, we deal with comparisons of the smallest and largest order statistics arising from independent heterogeneous generalized modified Weibull random variables in terms of various stochastic orderings. The main results established here are based on (i) vector majorization of parameters and (ii) multivariate chain majorization with heterogeneity in two and three parameters. KEYWORDSlikelihood ratio order, majorization, order statistics, series and parallel systems, stochastic orders 816

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On extreme order statistics from heterogeneous beta distributions with applications

Cited by 10 publications

References 26 publications

Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

Ordering Results on Extremes of Exponentiated Location-Scale Models

Ordering of series and parallel systems comprising heterogeneous generalized modified Weibull components

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