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Bayesian and maximum likelihood estimations from parameters of McDonald Extended Weibull model based on progressive type-II censoring

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Abstract

In recent years, there have been many efforts to develop a new statistical distribution with more flexibility that can be fitted well to complex data. In this article we consider the statistical inference of the six-parameter McDonald extended Weibull distribution (McEW) based on the progressively Type-II censored sample. The maximum likelihood estimates (MLEs) of the six parameters and their asymptotic distribution are obtained. Based on the asymptotic distribution, the asymptotic confidence limits of its parameters can be computed. We also propose bootstrap confidence intervals of the parameters. The Bayes estimates and the associated highest posterior density credible intervals are computed using the Markov-chain Monte Carlo (MCMC) method, including the Gibbs sampling technique and Metropolis-Hastings algorithm. Simulation experiments are performed to compare the proposed methods and the corresponding confidence intervals under the different censoring schemes. Finally, concluding remarks are given.

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References

  • Alexander, C., G. Cordeiro, E. Ortega, and J. M. Sarabia. 2012. Generalized beta generated distributions. Computational Statistics and Data Analysis 56 (6):1880–97.

    Article  MathSciNet  MATH  Google Scholar 

  • Balakrishnan, N. 2007. Progressive censoring methodology: An appraisal.Mathematics and Statistics 16 (2):211–59.

    MathSciNet  MATH  Google Scholar 

  • Balakrishnan, N., and E. Cramer. 2014. The art of progressive censoring: Applications to reliability and quality. New York: Birkhauser.

    Book  MATH  Google Scholar 

  • Balakrishnan, N., and R. A. Sandhu. 1995. A simple simulational algorithm for generating progressive Type-II censored samples. American Statistician 49 (2):229–30.

    Google Scholar 

  • Carrasco, M., E. M. Ortega, and G. M. Cordeiro. 2008. A generalized modified Weibull distribution for lifetime modeling. Computational Statistics and Data Analysis 53 (2):450–62.

    Article  MathSciNet  MATH  Google Scholar 

  • Chib, S., and E. Greenberg. 1995. Understanding the metropolis — Hastings algorithm. American Statistician 49 (4):327–335.

    Google Scholar 

  • Chung, Y., and C. Kim. 1997. Simultaneous estimation of the multivariate normal mean under balanced loss function. Communications in Statistics—Theory and Methods 26 (7): 1599–611.

    Article  MathSciNet  MATH  Google Scholar 

  • Cordeiro, G. M., and M. de Castro. 2011. A new family of generalized distributions. Journal of Statistical Computation and Simulation 81 (7): 883–98.

    Article  MathSciNet  MATH  Google Scholar 

  • Efron, B. 1982. The jackknife, bootstrap and other resampling plans. Philadelphia, PA: SIAM.

    Book  MATH  Google Scholar 

  • Eugene, N., C. Lee, and F. Famoye. 2002. Beta-normal distribution and its applications. Communications in Statistics—Theory and Methods 31 (4):497–512.

    Article  MathSciNet  MATH  Google Scholar 

  • Famoye, F., C. Lee, and O. Olumolade. 2005. The beta-Weibull distribution. Journal of Statistical Theory and Applications 4 (2):121–36.

    MathSciNet  Google Scholar 

  • Ghosh, M., M. J. Kim, and D. H. Kim. 2008. Constrained Bayes and empirical Bayes estimation under random effects normal ANOVA model with balanced loss function. Journal Statistical Planning and Inference 138 (7):2017–28.

    Article  MathSciNet  MATH  Google Scholar 

  • Hashimoto, E. M., E. M. M., Ortega, G. M. Cordeiro, and M. A. R. Pascoa. 2015. The McDonald extended Weibull distribution. Journal of Statistical Theory and Practice 9 (3):608–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Jung, J., and Y. Chung. 2013. Bayesian prediction of exponential Weibull distribution based on progressive type II censoring. Communications for Statistical Applications and Methods 20 (6):427–38.

    Article  Google Scholar 

  • Kim, C., J. Jung, and Y. Chung. 2011. Bayesian estimation for the exponentiated Weibull model type II progressive censoring. Statistical Papers 52 (1):53–70.

    Article  MathSciNet  MATH  Google Scholar 

  • Mudholkar, G. S., and D. K. Srivastava. 1993. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42 (2):299–302.

    Article  MATH  Google Scholar 

  • Mudholkar, G. S., D. K. Srivastava, and M. Freimer. 1995. The exponentiated Weibull family: A reanalysis of the bus-motor-failure data. Technometrics 37 (4):436–45.

    Article  MATH  Google Scholar 

  • Mudholkar, G. S., D. K. Srivastava, and G. D. Kollia. 1996. A generalization of the Weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association 91 (436):1575–83.

    Article  MathSciNet  MATH  Google Scholar 

  • Nassar, M. M., and F. H. Eissa. 2003. On the exponentiated Weibull distribution. Communications in Statistics—Theory and Methods 32 (7):1317–36.

    Article  MathSciNet  MATH  Google Scholar 

  • Nassar, M. M., and F. H. Eissa. 2005. Bayesian estimation for the exponentiated Weibull model. Communications in Statistics—Theory and Methods 33 (10):2343–62.

    Article  MathSciNet  MATH  Google Scholar 

  • Nicholas, M. D., and W. J. Padgett. 2006. A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International 22 (2):141–51.

    Article  Google Scholar 

  • Rodrigues, J., and A. Zellner. 1994. Weighted balanced loss function and estimation of the mean time to failure. Communications in Statistics—Theory and Methods 23 (12):3609–16.

    Article  MathSciNet  MATH  Google Scholar 

  • Silva, G. O., E. M. Ortega, and G. M. Cordeiro. 2010. The beta modified Weibull distribution. Lifetime Data Analysis 16 (3):409–30.

    Article  MathSciNet  MATH  Google Scholar 

  • Smith, R. L., and J. C. Naylor. 1987. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics 36 (3):358–69.

    Article  MathSciNet  Google Scholar 

  • Soliman, A. A., A. H. Abd-Ellah, N. A. Abou-Elheggag and E. A. Ahmed. 2012. Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data. Reliability Engineering and System Safety 100:48–57.

    Article  Google Scholar 

  • Soliman, A. A., A. H. Abd-Ellah, N. A., Abou-Elheggag, and E. A. Ahmed. 2013. Reliability estimation in stressstrength models: An MCMC approach. Journal of Theoretical and Applied Statistics 47 (4):715–28.

    MathSciNet  MATH  Google Scholar 

  • Sultan, K. S., N. H. Alsadat, and D. Kundu. 2013. Bayesian and maximum likelehood estimations of the inverse Weibull paparameters under progressive type-II censoring. Journal of Statistical Computation and Simulation 84 (10):2248–65.

    Article  Google Scholar 

  • Zellner, A. 1994. Bayesian and non-Bayesian estimation using balanced loss functions. In Statistical decision theory and related topics V, ed. S. S. Gupta and J. O. Berger, 377–90. New York: Springer-Verlag.

    Chapter  MATH  Google Scholar 

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Authors and Affiliations

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

    Sanghun Sel, Myoungjin Jung & Younshik Chung

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  1. Sanghun Sel
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  2. Myoungjin Jung
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  3. Younshik Chung
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Correspondence to Younshik Chung.

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Sel, S., Jung, M. & Chung, Y. Bayesian and maximum likelihood estimations from parameters of McDonald Extended Weibull model based on progressive type-II censoring. J Stat Theory Pract 12, 231–254 (2018). https://doi.org/10.1080/15598608.2017.1343693

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  • DOI: https://doi.org/10.1080/15598608.2017.1343693

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