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Estimation of \(P(Y > X)\) for the Weibull distribution

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Abstract

The estimation of \(P(Y > X)\) is studied when X and Y are independent Weibull random variables taking arbitrary parameter values. Three point and three interval estimators are derived. Their performance with respect to relative biases, relative mean squared errors, coverage probabilities, and coverage lengths is assessed by simulation studies and a real data application.

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Acknowledgements

The authors thank the editor and the two referees for their helpful comments, which contributed greatly to improve this paper.

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Authors and Affiliations

  1. University of Manchester, Manchester, M13 9PL, UK

    Saralees Nadarajah

  2. National University of Defense Technology, Hunan, 410073, People’s Republic of China

    Xiang Jia

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  1. Saralees Nadarajah
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  2. Xiang Jia
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Correspondence to Saralees Nadarajah.

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Nadarajah, S., Jia, X. Estimation of \(P(Y > X)\) for the Weibull distribution. Int J Syst Assur Eng Manag 8 (Suppl 2), 1762–1774 (2017). https://doi.org/10.1007/s13198-017-0666-9

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  • DOI: https://doi.org/10.1007/s13198-017-0666-9

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