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Bayesian inference and life testing plans for generalized exponential distribution

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Abstract

Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.

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References

  1. Gupta R D, Kundu D. Generalized exponential distribution. Aust N Z J Stat, 41: 173–188 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Gupta R D, Kundu D. Generalized exponential distribution: existing methods and some recent developments. J Statist Plann Infer, 137(11): 3537–3547 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Madi M T, Raqab M Z. Bayesian prediction of rainfall records using the generalized exponential distribution. Environmetrics, 18: 541–549 (2007)

    Article  MathSciNet  Google Scholar 

  4. Kundu D, Pradhan B. Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Commun Statist Theory Methods, to appear (2009)

  5. Mitra S, Kundu D. Analysis of the left censored data from the generalized exponential distribution. J Statist Comput Simul, 78(7): 669–679 (2008)

    Article  MATH  Google Scholar 

  6. Balakrishnan N, Aggrawala R. Progressive Censoring, Theory, Methods and Applications. Boston: Birkhäuser, 2000

    Google Scholar 

  7. Balakrishnan N. Progressive censoring methodology: an appraisal (with discussions). Test, 16(2): 211–296 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Pradhan B, Kundu D. On progressively censored generalized exponential distribution. Test, DOI:10.1007/s1 1749-008-0110-1

  9. Zhang Y, Meeker W Q. Bayesian life test planning for the Weibull distribution with given shape parameter. Metrika, 61: 237–249 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  11. Berger J O, Sun D. Bayesian analysis for the PolyWeibull distribution. J Amer Statist Assoc, 88: 1412–1418 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Son Y S, Oh M. Bayes estimation of the two-parameter gamma distribution. Commun Statist Theory Methods, 35: 285–293 (2006)

    MATH  MathSciNet  Google Scholar 

  13. Balakrishnan N, Sandhu R A. A simple algorithm for generating progressively type-II generated samples. Amer Statist, 49: 229–230 (1995)

    Article  Google Scholar 

  14. Lawless J F. Statistical Models and Methods for Lifetime Data, 2nd ed. New York: John Wiley and Sons, 2003

    MATH  Google Scholar 

  15. Balasooriya U, Balakrishnan N. Reliability sampling plan for log-normal distribution. IEEE Trans Reliability, 49: 199–203 (2000)

    Article  Google Scholar 

  16. Ng T, Chan C S, Balakrishnan N. Optimal progressive censoring plans for the Weibull distribution. Technometrics, 46: 470–481 (2004)

    Article  MathSciNet  Google Scholar 

  17. Gupta R D, Kundu D. Comparison of the Fisher information matrices of the Weibull and GE distributions. J Statist Plann Infer, 136(9): 3130–3144 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Debasis Kundu

  2. Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India

    Biswabrata Pradhan

Authors
  1. Debasis Kundu
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  2. Biswabrata Pradhan
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Corresponding author

Correspondence to Debasis Kundu.

Additional information

Dedicated to Professor Zhidong Bai on the occasion of his 65th birthday

This work was partially supported by a grant from the Department of Science and Technology, Government of India

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Kundu, D., Pradhan, B. Bayesian inference and life testing plans for generalized exponential distribution. Sci. China Ser. A-Math. 52, 1373–1388 (2009). https://doi.org/10.1007/s11425-009-0085-8

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  • DOI: https://doi.org/10.1007/s11425-009-0085-8

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