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Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data

  • Lee, Kyeongjun (Department of Computer Science and Statistics, Daegu University)
  • Received : 2017.03.03
  • Accepted : 2017.04.19
  • Published : 2017.05.31

Abstract

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

Keywords

References

  1. Blischke, W. R. and Murthy, D. N. P. (2000). Reliability : Modeling, prediction, and optimization. Wiley, New York.
  2. Cho, Y., Sun, H. and Lee, K. (2014). An estimation of the entropy for a Rayleigh distribution based on doubly-generalized Type-II hybrid censored samples. Entropy, 16, 3655-3669. https://doi.org/10.3390/e16073655
  3. Cho, Y., Sun, H. and Lee, K. (2015a). Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy, 17, 101-122.
  4. Cho, Y., Sun, H. and Lee, K. (2015b). Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. Statistical Methodology, 23, 18-34. https://doi.org/10.1016/j.stamet.2014.09.002
  5. Cover, T. M. and Thomas, J. A. (2005). Elements of information theory. Wiley: Hoboken, NJ, USA.
  6. Kang, S., Cho, Y., Han, J. and Kim, J. (2012). An estimation of the entropy for a double exponential distribution based on multiply Type-II censored samples. Entropy, 14, 161-173. https://doi.org/10.3390/e14020161
  7. Keller, A. Z., Giblin, M. T. and Farnworth, N. R. (1985). Reliability analysis of commercial vehicle engines. Reliability Engineering, 10, 89-102.
  8. Khan, M. S., Pasha, G. R. and Pasha, A. H. (2008). Theoretical analysis of inverse weibull distribution. Issue 2, 7, 30-38.
  9. Kwon, B., Lee, K. and Cho, Y. (2014). Estimation for the Rayleigh distribution based on Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 431-438. https://doi.org/10.7465/jkdi.2014.25.2.431
  10. Lee, K. and Cho, Y. (2015). Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data. Journal of the Korean Data & Information Science Society, 26, 1573-1582. https://doi.org/10.7465/jkdi.2015.26.6.1573
  11. Lee, K., Sun, H. and Cho, Y. (2014). Estimation of the exponential distribution based on multiply Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 633-641. https://doi.org/10.7465/jkdi.2014.25.3.633
  12. Shin, H., Kim, J. and Lee, C. (2014). Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 1581-1589. https://doi.org/10.7465/jkdi.2014.25.6.1581
  13. Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of American Statistical Association, 81, 82-86. https://doi.org/10.1080/01621459.1986.10478240

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