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Sequential order statistics with an order statistics prior

Author

Listed:
  • Burkschat, M.
  • Kamps, U.
  • Kateri, M.

Abstract

In the model of sequential order statistics, prior distributions are considered for the model parameters, which, for example, describe increasing load put on remaining components. Gamma priors are examined as well as priors out of a class of extended truncated Erlang distributions (ETED), which is introduced along with some properties. The choice of independent priors in both set-ups leads to respective independent, conjugate posterior distributions for the model parameters of sequential order statistics. Since, in practical applications, the model parameters will often be increasingly ordered, a multivariate prior is applied being the joint distribution of common ETED-order statistics. Whatever baseline distribution of the sequential order statistics is chosen, the joint posterior distribution turns out to be a Weinman multivariate exponential distribution. Posterior moments are given explicitly, and HPD credible sets for the model parameters are stated.

Suggested Citation

  • Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1826-1836
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    References listed on IDEAS

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    Cited by:

    1. Burkschat, Marco & Torrado, Nuria, 2014. "On the reversed hazard rate of sequential order statistics," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 106-113.
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    3. 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.
    4. Stefan Bedbur & Udo Kamps, 2019. "Testing for Equality of Parameters from Different Load-Sharing Systems," Stats, MDPI, vol. 2(1), pages 1-19, January.

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