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Estimation of $$P(X>Y)$$ P ( X > Y ) for Weibull distribution based on hybrid censored samples

Author

Listed:
  • A. Asgharzadeh

    (University of Mazandaran)

  • M. Kazemi

    (University of Mazandaran)

  • D. Kundu

    (Indian Institute of Technology)

Abstract

A hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. Based on hybrid censored samples, this paper deals with the inference on $$R = P(X>Y)$$ R = P ( X > Y ) , when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape parameter. The maximum likelihood estimator (MLE), and the approximate MLE of R are obtained. The asymptotic distribution of the MLE of R is obtained. Based on the asymptotic distribution, the confidence interval of R is constructed. Two bootstrap confidence intervals are also proposed. We consider the Bayesian estimate of R, and propose the corresponding credible interval for R. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a real data set has also been presented for illustrative purposes.

Suggested Citation

  • A. Asgharzadeh & M. Kazemi & D. Kundu, 2017. "Estimation of $$P(X>Y)$$ P ( X > Y ) for Weibull distribution based on hybrid censored samples," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 489-498, January.
    • Handle: RePEc:spr:ijsaem:v:8:y:2017:i:1:d:10.1007_s13198-015-0390-2
    DOI: 10.1007/s13198-015-0390-2
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    References listed on IDEAS

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    1. Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
    2. Adimari, Gianfranco & Chiogna, Monica, 2006. "Partially parametric interval estimation of Pr{Y>X}," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1875-1891, December.
    3. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    4. Debasis Kundu & Rameshwar D. Gupta, 2005. "Estimation of P[Y > X] for generalized exponential distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 291-308, June.
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