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Inference from multiple samples of Weibull sequential order statistics

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  • Bedbur, Stefan
  • Johnen, Marcus
  • Kamps, Udo

Abstract

In a set-up of independent samples of sequential order statistics from Weibull distributions, which may describe a load-sharing lifetime experiment, statistical inference is considered for scale parameters and a common shape parameter. A representation of the corresponding Fisher information matrix is stated, and the joint maximum likelihood estimator is shown to be strongly consistent and asymptotically efficient. Multivariate tests are developed and analyzed, including tests on homogeneity of the scale parameters, which indicate whether the model of common order statistics has to be rejected, and tests on an underlying exponential distribution. Some results are applied to two real data sets known from the literature. In a load-sharing interpretation and within the model of sequential order statistics, the intention is to detect, confirm and quantify load-sharing effects based on multiple samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:381-399
    DOI: 10.1016/j.jmva.2018.10.010
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    References listed on IDEAS

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    1. 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.
    2. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    3. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    4. Paul H. Kvam & Edsel A. Pena, 2005. "Estimating Load-Sharing Properties in a Dynamic Reliability System," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 262-272, March.
    5. 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.
    6. 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.
    7. Eric Beutner, 2008. "Nonparametric inference for sequential k-out-of-n systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 605-626, 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.

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