Generalized Order Statistics

Kamps, Udo

doi:10.1002/9781118445112.stat00832.pub2

Cited by 12 publications

(4 citation statements)

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“…Linear unbiased prediction of future Pareto record values is discussed in Paul and Thomas (2016), and maximum likelihood prediction of future Pareto record values is studied in Raqab (2007). Since the model of record values is contained in the generalized order statistics model [see Kamps (1995Kamps ( , 2016], all results pertaining to prediction of future generalized order statistics can be specialized to solve the prediction problem for record values [see, e.g., Burkschat (2009)]. Bayesian prediction methods for future record values were first discussed by Dunsmore (1983) and have subsequently been applied to various distribution families [cf.…”

Section: Introductionmentioning

confidence: 99%

Maximum product of spacings prediction of future record values

Volovskiy

Kamps

2020

Metrika

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A spacings-based prediction method for future upper record values is proposed as an alternative to maximum likelihood prediction. For an underlying family of distributions with continuous cumulative distribution functions, the general form of the predictor as a function of the estimator of the distributional parameters is established. A connection between this method and the maximum observed likelihood prediction procedure is shown. The maximum product of spacings predictor turns out to be useful to predict the next record value in contrast to likelihood-based procedures, which provide trivial predictors in this particular case. Moreover, examples are given for the exponential and the Pareto distributions, and a real data set is analyzed.

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Section: Introductionmentioning

confidence: 99%

Maximum product of spacings prediction of future record values

Volovskiy

Kamps

2020

Metrika

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“…Due to this connection, many statistical and probabilistic results have been established using generalized order statistics as a unifying account to ordered data. A review as well as many references are provided by Cramer (2003) and Kamps (2016). Dual generalized order statistics leading to a general account for decreasingly ordered data have been introduced in Burkschat et al (2003).…”

Section: Generalized Order Statisticsmentioning

confidence: 99%

Ordered and censored lifetime data in reliability: An illustrative review

Cramer

2021

WIREs Computational Stats

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“…. , n}; see References [1,24]. In the distribution-theoretical sense, order statistics (based on F 1 ) are included in the model and result by setting F 1 = · · · = F n .…”

Section: Model and Basic Propertiesmentioning

confidence: 99%

Testing for Equality of Parameters from Different Load-Sharing Systems

Bedbur

Kamps

2019

Stats

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In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k-out-of-n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures.

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Generalized Order Statistics

Cited by 12 publications

References 100 publications

Maximum product of spacings prediction of future record values

Maximum product of spacings prediction of future record values

Ordered and censored lifetime data in reliability: An illustrative review

Testing for Equality of Parameters from Different Load-Sharing Systems

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