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Bayesian estimation of P (Y<X) from Burr-type X model containing spurious observations

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Abstract

We consider the problem of estimating R=P(Y<X) when X and Y are independent Burr-type X random variables. We assume that the sample from each population contains one spurious observation. Bayes estimates are derived for exchangeable and identifiable cases. Monte Carlo simulation is carried out to compare the bias and the expected loss of R.

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References

  1. Ahmad, K.E., Fakhry, M.E. and Jaheen, Z.F. (1997) Empirical Bayes estimation of P(Y<X) and charaterizations of Burr-type X model, Journal of Statistical Planning and Inference, 64, 297–308.

    Article  MATH  MathSciNet  Google Scholar 

  2. Burr, I.W. (1942) Cumulative frequency functions, Annals of Mathematical Statistics, 13, 215–232.

    MATH  MathSciNet  Google Scholar 

  3. Church, J.D. and Harris, B. (1970) The estimation of reliability from stress strength relationship, Technometrics, 12, 49–54.

    Article  MATH  Google Scholar 

  4. Enis, P. and Geisser, S. (1971) Estimation of the probability that P(Y<X). Journal of the American Statistical Association, 66, 162–168.

    Article  MATH  MathSciNet  Google Scholar 

  5. Jaheen, Z.E. (1995) Bayesian approach to prediction with outliers from the Burr type X model. Microelectron. reliab., 35, 45–47.

    Article  Google Scholar 

  6. Jaheen, Z.E. (1996) Empirical Bayes estimation of the reliability and failure rate functions of the Burr type X failure model, Journal of Applied Statistical Science, 3, 281–288.

    MATH  MathSciNet  Google Scholar 

  7. Jeevanand, E.S. and Nair N.U. (1994) Estimating P(Y<X) from exponential samples containing spurious observations, Communications in Statistics—Theory and Methods, 23, 2629–2642.

    MATH  MathSciNet  Google Scholar 

  8. Kale, V.B. and Kale, B.K. (1992) Outliers in exponential sample—A Bayesian approach. Gujarat Statistical Review, Khatri memorial vol.

  9. Weerahandi, S. and Johnson, R.A. (1992) Testing reliability in a stress-strength model when X and Y are normally distributed, Techometrics, 34, 38–91.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Kongju National University, 314-701, Kongju, Korea

    Chansoo Kim

  2. Department of Statistics, Pusan National University, 609-735, Pusan, Korea

    Younshik Chung

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  1. Chansoo Kim
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  2. Younshik Chung
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Kim, C., Chung, Y. Bayesian estimation of P (Y<X) from Burr-type X model containing spurious observations. Statistical Papers 47, 643–651 (2006). https://doi.org/10.1007/s00362-006-0310-2

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  • DOI: https://doi.org/10.1007/s00362-006-0310-2

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