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Distances between models of generalized order statistics

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  • Vuong, Q.N.
  • Bedbur, S.
  • Kamps, U.

Abstract

The concept of generalized order statistics is a distribution theoretical set-up, which contains a variety of models for ordered data as particular cases, such as common order statistics, sequential order statistics, progressively type-II censored order statistics, record values, kth record values, and Pfeifer record values. In order to quantify the structure of generalized order statistics, distances between different respective models are measured by means of explicit expressions for divergences and distances applied to joint densities of ordered random variables. The results are exemplarily utilized to find a closest common order statistics model to some given model of sequential order statistics. Moreover, statistical applications in reliability are shown.

Suggested Citation

  • Vuong, Q.N. & Bedbur, S. & Kamps, U., 2013. "Distances between models of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 24-36.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:24-36
    DOI: 10.1016/j.jmva.2013.03.010
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    References listed on IDEAS

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    1. Cramer, Erhard & Kamps, Udo & Rychlik, Tomasz, 2002. "On the existence of moments of generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 397-404, October.
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    5. Balakrishnan, N. & Beutner, E. & Kamps, U., 2008. "Order restricted inference for sequential k-out-of-n systems," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1489-1502, August.
    6. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    7. Erhard Cramer & Udo Kamps & Tomasz Rychlik, 2004. "Unimodality of uniform generalized order statistics, with applications to mean bounds," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 183-192, March.
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    12. N. Balakrishnan & U. Kamps & M. Kateri, 2012. "A sequential order statistics approach to step-stress testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 303-318, April.
    13. Erhard Cramer & Udo Kamps, 1996. "Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 535-549, September.
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    Cited by:

    1. Alexander Katzur & Udo Kamps, 2020. "Classification using sequential order statistics," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 201-230, March.
    2. Bedbur, S. & Kamps, U., 2019. "Confidence regions in step–stress experiments with multiple samples under repeated type-II censoring," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 181-186.
    3. Marcus Johnen & Stefan Bedbur & Udo Kamps, 2020. "A note on multiple roots of a likelihood equation for Weibull sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 519-525, May.
    4. Bedbur, Stefan & Johnen, Marcus & Kamps, Udo, 2019. "Inference from multiple samples of Weibull sequential order statistics," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 381-399.
    5. Katzur, Alexander & Kamps, Udo, 2016. "Classification into Kullback–Leibler balls in exponential families," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 75-90.

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