Stochastic Comparisons of Generalized Order Statistics

Belzunce, Félix; Mercader, José-Angel; Ruiz, José-María

doi:10.1017/s0269964805050072

Cited by 69 publications

(54 citation statements)

References 5 publications

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“…, n. The HR ordering property of SOS in the PHR model was established in Theorem 4.5 of Cramer and Kamps [13]. Further ordering results in the PHR model were presented in Belzunce et al [3]. In this case, it is well known that SOS are generalized order statistics (GOS) and Cramer et al [14] proved that GOS are LR ordered (see also Hu and Zhuang [18]).…”

Section: Remark 32mentioning

confidence: 91%

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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Abstract:The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k-out-of-n systems. In particular, we show that they are not necessarily hazard rate ordered.

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Section: Remark 32mentioning

confidence: 91%

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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“…Hu et al [11] extend a result for spacings based on non-identically distributed exponential random variables and deal with stochastic comparisons. Results on stochastic comparisons of spacings of generalized order statistics can be found in [12][13][14][15]. In the following, we prove an extension of the result of Karlin and Rinott [5] to spacings of generalized order statistics.…”

Section: Introductionmentioning

confidence: 61%

Multivariate dependence of spacings of generalized order statistics

Burkschat

2009

Journal of Multivariate Analysis

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Multivariate total positivity Strongly multivariate reverse regular rule Conditionally increasing in sequence Negative and positive orthant dependence Right tail increasing in sequence Increasing failure rate Reversed hazard rate Non-negativity of BLUE Dual generalized order statistics a b s t r a c t Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the underlying distribution, stronger dependence relations are established.For instance, if the model parameters are decreasingly ordered and the underlying distribution has a log-convex decreasing (log-concave) hazard rate, then the spacings satisfy the MTP 2 (S-MRR 2 ) property. Some consequences of the results are given. In particular, conditions for non-negativity of the best linear unbiased estimator of the scale parameter in a location-scale family are obtained. By applying a result for dual generalized order statistics, we show that in the particular situation of usual order statistics the assumptions can be weakened.

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“…Let m = −1 and k ∈ N, then the model of kth record 327 values is obtained. Choosing the parameters appropriately, several other models of ordered rv's are seen to be particular cases, see [2,10,17]. …”

Section: Generalized Order Statisticsmentioning

confidence: 99%

“…Readers can refer to [8][9][10][11][12][13] to obtain stochastic comparisons of GOSs and their spacings by analogy with ordinary order statistics. For the aging preservations of spacings of GOSs, readers can refer to [13][14].…”

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confidence: 99%

Some comparisons between generalized order statistics

Qiu

Wang

2007

Appl. Math. Chin. Univ.

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Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics. §1 IntroductionThe concept of generalized order statistics was introduced by Kamps [1-2] as a unified approach to a variety of models of ordered random variables (rv's). Choosing the parameters approximately, several other models of ordered rv's, such as ordinary order statistics, sequential order statistics, k-record values, etc, are seen to be the particular cases. Generalized order statistics (GOS) have been of interest in the past ten years because they are more flexible in reliability theory, statistical modeling and inference, see [3][4][5][6][7].A natural question for GOSs is whether it possesses analogical properties of ordinary order statistics. Readers can refer to [8][9][10][11][12][13] to obtain stochastic comparisons of GOSs and their spacings by analogy with ordinary order statistics. For the aging preservations of spacings of GOSs, readers can refer to [13][14]. Recently, Wang and Li [15] exhibited preservations of ordinary order statistics under some stochastic orders; Qiu and Shen [16] found that expectations of spacings between the first two ordinary order statistics and between the last two ordinary order statistics will increase under suitable conditions.The first purpose of this paper, after recalling the definitions of generalized order statistics, some stochastic orders and three useful lemmas in §2, is to build some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier

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Stochastic Comparisons of Generalized Order Statistics

Cited by 69 publications

References 5 publications

Coherent systems based on sequential order statistics

Coherent systems based on sequential order statistics

Multivariate dependence of spacings of generalized order statistics

Some comparisons between generalized order statistics

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