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Statistical Papers

, Volume 52, Issue 1, pp 53–70 | Cite as

Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring

  • Chansoo Kim
  • Jinhyouk Jung
  • Younshik ChungEmail author
Regular Article

Abstract

Based on progressive Type II censored samples, we have derived the maximum likelihood and Bayes estimators for the two shape parameters and the reliability function of the exponentiated Weibull lifetime model. We obtained Bayes estimators using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions. This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Stadistca 21, 223–237, 1980) method for obtaining Bayes estimates under these loss functions. We made comparisons between these estimators and the maximum likelihood estimators using a Monte Carlo simulation study.

Keywords

Bayesian estimation Exponentiated Weibull distribution Linex loss function Lindley approximation Maximum likelihood estimator Progressive Type II censoring Squared error loss function 

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References

  1. Aggarwala R (2001) Progressive censoring. In: Balakrishnan N, Rao CR (eds) Handbook of statistics 20: advances in reliabilityGoogle Scholar
  2. Balakrishnan N, Sandhu RA (1995) A simple simulation algorithm for generating progressive Type II censored samples. Am Stat 49(2): 229–230CrossRefGoogle Scholar
  3. Cohen AC (1963) Progressively censored samples in life testing. Technometrics 5: 327–339zbMATHCrossRefMathSciNetGoogle Scholar
  4. Jiang R, Murthy DNP (1999) The exponentiated Weibull family: a graphical approach. IEEE Trans Reliab 48(1): 68–72CrossRefGoogle Scholar
  5. Lindley DV (1980) Approximate Bayesian methods. Trabajos de Stadistca 21: 223–237MathSciNetGoogle Scholar
  6. Mann NR (1971) Best linear invariant estimation for Weibull parameter under progressive censoring. Technometrics 13: 521–534zbMATHCrossRefMathSciNetGoogle Scholar
  7. Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab R-42(2): 299–302CrossRefGoogle Scholar
  8. Mudholkar GS, Srivastava DK, Freimer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37(4): 436–445zbMATHCrossRefGoogle Scholar
  9. Mudholkar GS, Hutson AD (1996) The exponentiated Weibull family: some properties and a flood data application. Commun Stat Theory Methods 25(12): 3059–3083zbMATHCrossRefMathSciNetGoogle Scholar
  10. Nassar MM, Eissa FH (2003) On the exponentiated Weibull distribution. Commun Stat Theory Methods 32(7): 1317–1336zbMATHCrossRefMathSciNetGoogle Scholar
  11. Nassar MM, Eissa FH (2004) Bayesian estimation for the exponentiated Weibull model. Commun Stat Theory Methods 33(10): 2343–2362zbMATHMathSciNetGoogle Scholar
  12. Varian H (1975) A Bayesian approach to real estate assessment. North Holland, Amsterdam, pp 195–208Google Scholar
  13. Viveros R, Balakrishnan N (1994) Interval estimation of life characteristics from progressively Censored data. Technometric 36: 84–91zbMATHCrossRefMathSciNetGoogle Scholar
  14. Zellner A (1986) Bayesian estimation and prediction using asymmetric loss function. J Am Stat Assoc 81: 446–451zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsKongju National UniversityKongjuKorea
  2. 2.Department of StatisticsPusan National UniversityPusanKorea

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