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On the reversed hazard rate of sequential order statistics

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  • Burkschat, Marco
  • Torrado, Nuria

Abstract

Sequential order statistics can be used to describe the lifetime of a system with n components which works as long as k components function assuming that failures possibly affect the lifetimes of remaining units. In this work, the reversed hazard rates of sequential order statistics are examined. Conditions for the reversed hazard rate ordering and the decreasing reversed hazard rate property of sequential order statistics are given.

Suggested Citation

  • Burkschat, Marco & Torrado, Nuria, 2014. "On the reversed hazard rate of sequential order statistics," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 106-113.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:106-113
    DOI: 10.1016/j.spl.2013.11.015
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Asok Nanda & Moshe Shaked, 2001. "The Hazard Rate and the Reversed Hazard Rate Orders, with Applications to Order Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 853-864, December.
    6. 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.
    7. Nuria Torrado & Rosa E. Lillo & Michael P. Wiper, 2012. "Sequential Order Statistics: Ageing and Stochastic Orderings," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 579-596, September.
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    Cited by:

    1. Tzong-Ru Tsai & Hua Xin & Chiun-How Kao, 2021. "Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    2. Daron Acemoglu & Ali Makhdoumi & Azarakhsh Malekian & Asu Ozdaglar, 2022. "Too Much Data: Prices and Inefficiencies in Data Markets," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 218-256, November.
    3. Markos V. Koutras & Ioannis S. Triantafyllou & Serkan Eryilmaz, 2016. "Stochastic Comparisons Between Lifetimes of Reliability Systems with Exchangeable Components," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1081-1095, December.
    4. Tzong-Ru Tsai & Yuhlong Lio & Hua Xin & Hoang Pham, 2021. "Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution," Mathematics, MDPI, vol. 9(8), pages 1-17, April.

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