Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation of the Exponential Distributions based on Multiply Progressive Type II Censored Sample

  • Received : 2012.06.05
  • Accepted : 2012.08.03
  • Published : 2012.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). 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 MLE and $AMLE_I$ in the sense of the MSE.

Keywords

References

  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 Sandu, R. A. (1995). A simple simulation algorithm for generating progressively Type II censored samples, The American Statistician, 49, 229-230.
  3. Balakrishnan, N. and Sandu, R. A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type II censored sample, Sanky a: The Indian Journal of Statistics, 58, 1-9.
  4. Chen, D. G. and Lio, Y. L. (2010). Parameter estimation for generalized exponential distribution under progressive Type I interval censoring, Computational Statistics and Data Analysis, 54, 1581-1591. https://doi.org/10.1016/j.csda.2010.01.007
  5. Herd, R. G. (1956). Estimation of the Parameters of a Population from a Multi-Censored Sample, Ph. D. Thesis, Iowa State College, Ames, Iowa.
  6. Kang, S. B. (2003). Approximate MLEs for exponential distribution under multiply Type II censoring, Journal of the Korean Data and Information Science Society, 14, 983-988.
  7. Kang, S. B. and Cho, Y. S. (1998). MRE for exponential distribution under general progressive Type II censored samples, Journal of the Korean Data and Information Science Society, 9, 71-76.
  8. 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
  9. Nelson, W. (1982). Applied Life Data Analysis, John Wiley and Sons, New York.
  10. 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 and Information Science Society, 21, 927-934.
  11. 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.

Cited by

  1. Estimation of the exponential distribution based on multiply Type I hybrid censored sample vol.25, pp.3, 2014, https://doi.org/10.7465/jkdi.2014.25.3.633
  2. Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample vol.25, pp.6, 2014, https://doi.org/10.7465/jkdi.2014.25.6.1581