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Estimation of the exponential distribution based on multiply Type I hybrid censored sample

  • Lee, Kyeongjun (Department of Statistics, Pusan National University) ;
  • Sun, Hokeun (Department of Statistics, Pusan National University) ;
  • Cho, Youngseuk (Department of Statistics, Pusan National University)
  • 투고 : 2014.03.13
  • 심사 : 2014.04.12
  • 발행 : 2014.05.31

초록

The exponential distibution is one of the most popular distributions in analyzing the lifetime data. In this paper, we propose multiply Type I hybrid censoring. And this paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply Type I hybrid censoring. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator (MLE) of the scale parameter ${\sigma}$ under the proposed multiply Type I hybrid censored samples. We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The $AMLE_{II}$ is better than $AMLE_I$ in the sense of the RMSE.

키워드

참고문헌

  1. Asgharzadeh, A. (2009). Approximate MLE for the scaled generalized exponential distribution under progressive Type II censoring. Journal of the Korean Statistical Society, 38, 223-229. https://doi.org/10.1016/j.jkss.2008.09.004
  2. Balakrishnan, N. and Cohen, A. C. (1991). Order statistics and inference: Estimation methods, Academic Press, Boston.
  3. Balakrishnan, N. and Sandu, R. A. (1996). Best linear unbiased and maximum mlikelihood estimation for exponential distributions under general progressive Type II censored sample. Sanky A: The Indian Journal of Statistics, 58, 1-9.
  4. Cho, Y. S., Lee, C. S. and Shin, H. J. (2013). Estimation for the generalized exponential distribution under progressive type I interval censoring. Journal of the Korean Data & Information Science Society, 24, 1309-1317. https://doi.org/10.7465/jkdi.2013.24.6.1309
  5. Epstein, B. (1954). Truncated life tests in the exponential case. Annals of Mathematical Statistics, 25, 555-564. https://doi.org/10.1214/aoms/1177728723
  6. Kang, J. H. and Lee, C. S. (2013). Estimations of the skew parameter in a skewed double power function distribution. Journal of the Korean Data & Information Science Society, 24, 901-909. https://doi.org/10.7465/jkdi.2013.24.4.901
  7. Kang, S. B. (2003). Approximate MLEs for exponential distribution under multiply Type II censoring. Journal of the Korean Data & Information Science Society, 14, 983-988.
  8. Kang, S. B. and Cho, Y. S. (1998). MRE for exponential distirubion under general progressive Type II censored samples. Journal of the Korean Data & Information Science Society, 9, 71-76.
  9. Kang, S. B. and Park, S. M. (2005). Estimation for the exponentiated exponential distribution based on multiply Type II censored samples. The Korean Communications in Statistics, 12, 643-652. https://doi.org/10.5351/CKSS.2005.12.3.643
  10. Lee, J. C. and Lee, C. S. (2012). An approximate maximum likelihood estimator in a weighted exponential distribution. Journal of the Korean Data & Information Science Society, 23, 219-225. https://doi.org/10.7465/jkdi.2012.23.1.219
  11. Lee, K. J., Park, C. K. and Cho, Y. S. (2012). Estimation of the exponential distribution based on multiply progressive Type II censored sample. The Korean Communications in Statistics, 19, 697-704. https://doi.org/10.5351/CKSS.2012.19.5.697
  12. Nelson, W. (1982). Applied life data analysis, John Wiley & Sons, New York.
  13. Shin, H. J., Lee, K. H. and Cho, Y. S. (2010). Parameter estimation for exponential distribution under progressive Type I interval censoring. Journal of the Korean Data & Information Science Society, 21, 927-934.
  14. Singh, U. and Kumar, A. (2007). Bayesian estimation of the exponential parameter under a multiply Type II censoring scheme. Austrian Journal of Statistics, 36, 227-238.

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