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Estimation and Prediction for Flexible Weibull Distribution Based on Progressive Type II Censored Data

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Abstract

In this work, we consider the problem of estimating the parameters and predicting the unobserved or removed ordered data for the progressive type II censored flexible Weibull sample. Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems. The likelihood method as well as the Bayesian sampling techniques is applied for the inference problems. The point predictors and credible intervals of unobserved data based on an informative set of data are computed. Markov Chain Monte Carlo samples are performed to compare the so-obtained methods, and one real data set is analyzed for illustrative purposes.

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References

  1. Aarset, M.V.: How to identify bathtub hazard rate. IEEE Trans. Reliab. 36, 106–108 (1978)

    MATH  Google Scholar 

  2. Ahmad, Z., Hussain, Z.: Flexible Weibull distribution. J. Comput. Math. Sci. 8(6), 251–260 (2017)

    Google Scholar 

  3. Al-Hussaini, E.K.: Predicting observable from a general class of distributions. J. Stat. Plan. Inference 79, 79–81 (1999)

    Article  MathSciNet  Google Scholar 

  4. Balakrishnan, N., Aggrawala, R.: Progressive Censoring, Theory, Methods and Applications. Birkhauser, Boston (2000)

    Book  Google Scholar 

  5. Bebbington, M., Lai, C.D., Zitikis, R.: A flexible Weibull extension. Reliab. Eng. Syst. Saf. 92, 719–726 (2007a)

    Article  Google Scholar 

  6. Bebbington, M., Lai, C.D., Zitikis, R.: Modeling human mortality using mixtures of bathtub shaped failure rate distributions. J. Theor. Biol. 245, 528–538 (2007b)

    Article  Google Scholar 

  7. Casella, G., Berger, R.: Statistical Inference, 2nd edn. Duxbury, New York (2002)

    MATH  Google Scholar 

  8. Chen, M.H., Shao, Q.M., Ibrahim, J.G.: Monte Carlo Methods in Bayesian Computation. Springer, New York (2000)

    Book  Google Scholar 

  9. Choqueta, R., Guédonb, Y., Besnarda, A., Guillemainc, M., Pradel, R.: Estimating stop over duration in the presence of trap-effects R. Ecol. Modell. 250, 111–118 (2013)

    Article  Google Scholar 

  10. Cohen, A.C.: Progressively censored samples in life testing. Technometrics 5, 327–329 (1963)

    Article  MathSciNet  Google Scholar 

  11. Dahlquist, G., Björck, Å.: Numerical methods in scientific computing, Volume I, SIAM (2007)

  12. David, H.A., Nagaraja, H.N.: Order Statistics, 3rd edn. Wiley, New York (2003)

    Book  Google Scholar 

  13. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)

    Article  MathSciNet  Google Scholar 

  14. Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distribution, 2nd edn. Wiley and Sons, New York (1995)

    MATH  Google Scholar 

  15. Kaminsky, M.P., Krivtsov, V.V.: A simple procedure for Bayesian estimation of the Weibull distribution. IEEE Trans. Reliab. 54, 612–616 (2005)

    Article  Google Scholar 

  16. Kaminsky, K.S., Nelson, P.I.: Prediction of order statistics. In: Balakrishnan, N., Rao, C.R. (eds.) Hand book of statistics, order statistics: applications, vol. 17, pp. 431–450. North-Holland, Amsterdam (1998)

  17. Kaminsky, K.S., Rhodin, L.S.: Maximum likelihood prediction. Ann. Inst. Stat. Math. 37, 707–717 (1985)

    Article  MathSciNet  Google Scholar 

  18. Kim, C., Jung, J., Chung, Y.: Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring. Stat. Pap. 52(1), 53–70 (2011)

    Article  MathSciNet  Google Scholar 

  19. Kundu, D.: Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring. Technometrics 50, 144–154 (2008)

    Article  MathSciNet  Google Scholar 

  20. Kundu, D., Raqab, M.Z.: Bayesian inference and prediction for a Type-II censored Weibull distribution. J. Stat. Plan. Inference 142(1), 41–47 (2012)

    Article  MathSciNet  Google Scholar 

  21. Lawless, J.F.: Statistical Models and Methods for Life Time Data. Wiley, New York (1982)

    MATH  Google Scholar 

  22. Lehmann, E.L., Casella, G.: Theory of Point Estimation, 2nd edn. Springer, New York (1998)

    MATH  Google Scholar 

  23. Li, Y., Ghosh, S.K.: Efficient sampling methods for truncated multivariate normal and Student-t distributions subject to linear inequality constraints. J. Stat.Theory Pract. 9(4), 712–732 (2015). https://doi.org/10.1080/15598608.2014.996690

    Article  MathSciNet  MATH  Google Scholar 

  24. Madi, M.T., Raqab, M.Z.: Bayesian prediction of temperature records using the Pareto model. Environmetrics 15, 701–710 (2004)

    Article  Google Scholar 

  25. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)

    Article  Google Scholar 

  26. Murthy, D.N.P., Bulmer, M., Eccleston, J.A.: Weibull model selection for reliability modelling. Reliab. Eng. Syst. Saf. 86(3), 257–267 (2004)

    Article  Google Scholar 

  27. Romberg, W.: Vereinfachte numerische integration. Det Kongelige Norske Videnskabers Selskab Forhandlinger (Trondheim) 28(7), 30–36 (1955)

    MathSciNet  MATH  Google Scholar 

  28. Selim, M.A.: Bayesian estimations from the two-parameter bathtub-shaped lifetime distribution based on record values. Pak. J. Stat. Oper. Res. 8(2), 155–165 (2012)

    Article  MathSciNet  Google Scholar 

  29. Singh, S.K., Singh, U., Sharma, V.K.: Bayesian estimation and prediction for flexible Weibull model under TypeII censoring scheme. J. Probab. Stat. 2013, 1–16 (2013)

    Google Scholar 

  30. Suprawhardana, M.S., Prayoto, S.: Total time on test plot analysis for mechanical components of the RSG-GAS reactor. Atom Indones 25(2), 81–90 (1999)

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Acknowledgements

The authors would like to thank the editor and referees for their comments and very constructive suggestions that contributed to the improvement of this version of the paper.

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Authors and Affiliations

  1. Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan

    O. M. Bdair & M. F. M. Naser

  2. Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman, Jordan

    R. R. Abu Awwad & G. K. Abufoudeh

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  1. O. M. Bdair
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  2. R. R. Abu Awwad
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  3. G. K. Abufoudeh
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  4. M. F. M. Naser
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Correspondence to M. F. M. Naser.

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Bdair, O.M., Awwad, R.R.A., Abufoudeh, G.K. et al. Estimation and Prediction for Flexible Weibull Distribution Based on Progressive Type II Censored Data. Commun. Math. Stat. 8, 255–277 (2020). https://doi.org/10.1007/s40304-018-00173-0

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  • DOI: https://doi.org/10.1007/s40304-018-00173-0

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