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On progressively censored generalized exponential distribution

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Abstract

In this paper, we consider the statistical inference of the unknown parameters of the generalized exponential distribution in presence of progressive censoring. We obtain maximum likelihood estimators of the unknown parameters using EM algorithm. We also compute the expected Fisher information matrix using the missing value principle. We then use these values to determine the optimal progressive censoring plans. Different optimality criteria are considered, and selected optimal progressive censoring plans are presented. One example has been provided for illustrative purposes.

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References

  • Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover, New York

    MATH  Google Scholar 

  • Balakrishnan N (2007) Progressive censoring methodology: an appraisal. TEST 16(2):211–296 (with discussions)

    Article  MATH  MathSciNet  Google Scholar 

  • Balakrishnan N, Aggarwala R (2000) Progressive censoring, theory, methods and applications. Birkhauser, Boston

    Google Scholar 

  • Balakrishnan N, Kannan N (2001) Point and interval estimation for parameters of the logistic distribution based on progressively type-II censored data. In: Handbook of Statistics, vol 20. North Holland, Amsterdam

    Google Scholar 

  • Balakrishnan N, Sandhu RA (1995) A simple algorithm for generating progressively type-II generated samples. Am Stat 49:229–230

    Article  Google Scholar 

  • Balakrishnan N, Kannan N, Lin CT, Wu SJS (2004) Inference for the extreme value distribution under progressive type-II censoring. J Stat Comput Simul 25–45

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

    Article  Google Scholar 

  • Cohen AC (1963) Progressively censored samples in life testing. Technometrics 5:327–329

    Article  MATH  MathSciNet  Google Scholar 

  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via EM algorithm. J R Stat Soc, Ser B 39:1–38

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta RD, Kundu D (2001) Generalized exponential distribution: different methods of estimations. J Stat Comput Simul 69:315–338

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta RD, Kundu D (2006) Comparison of the Fisher information matrices of the Weibull and GE distributions. J Stat Plan Inference 136(9):3130–3144

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta RD, Kundu D (2007) Generalized exponential distribution; existing methods and some recent developments. J Stat Plan Inference 137:3537–3547

    Article  MATH  MathSciNet  Google Scholar 

  • Kundu D (2007) On hybrid censored Weibull distribution. J Stat Plan Inference 137:2127–2142

    Article  MATH  MathSciNet  Google Scholar 

  • Lawless JF (1982) Statistical models and methods for lifetime data. Wiley, New York

    MATH  Google Scholar 

  • Little RJA, Rubin DB (1983) Incomplete data. In: Kotz S, Johnson NL (eds) Encyclopedia of statistical sciences, vol 4. Wiley, New York, pp 46–53

    Google Scholar 

  • Louis TA (1982) Finding the observed information matrix using the EM algorithm. J R Stat Soc, Ser B 44:226–233

    MATH  MathSciNet  Google Scholar 

  • Mann NR (1971) Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics 13:521–533

    Article  MATH  MathSciNet  Google Scholar 

  • Ng T, Chan CS, Balakrishnan N (2002) Estimation of parameters from progressively censored data using EM algorithm. Comput Stat Data Anal 39:371–386

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Tanner MA (1993) Tools for statistical inferences: observed data and data augmentation methods, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Thomas DR, Wilson WM (1972) Linear order statistic estimation for the two-parameter Weibull and extreme value distributions from type-II progressively censored samples. Technometrics 14:679–691

    Article  MATH  Google Scholar 

  • Viveros R, Balakrishnan N (1994) Interval estimation of parameters of life from progressively censored data. Technometrics 36:84–91

    Article  MATH  MathSciNet  Google Scholar 

  • Wang BX, Yu K (2007) Optimum plan for step-stress model with progressive type-II censoring. TEST. doi:10.1007/s11749-007-0060-z

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. SQC & OR Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, Pin, 700108, India

    Biswabrata Pradhan

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

    Debasis Kundu

Authors
  1. Biswabrata Pradhan
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  2. Debasis Kundu
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Correspondence to Biswabrata Pradhan.

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Pradhan, B., Kundu, D. On progressively censored generalized exponential distribution. TEST 18, 497–515 (2009). https://doi.org/10.1007/s11749-008-0110-1

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  • DOI: https://doi.org/10.1007/s11749-008-0110-1

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