Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Estimation for the Rayleigh distribution based on Type I hybrid censored sample

  • Kwon, Byongwon (Digital Marketing Team, Shinsegae Department Store Centumcity) ;
  • Lee, Kyeongjun (Department of Statistics, Pusan National University) ;
  • Cho, Youngseuk (Department of Statistics, Pusan National University)
  • Received : 2014.01.08
  • Accepted : 2014.02.03
  • Published : 2014.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Type I hybrid censoring scheme is the combination of the Type I and Type II censoring scheme introduced by Epstein (1954). Epstein considered a hybrid censoring sampling scheme in which the life testing experiment is terminated at a random time $T^*$ which is the time that happens rst among the following two; time of the kth unit is observed or time of the experiment length set in advance. The likelihood function of this scheme from the Rayleigh distribution cannot be solved in a explicit solution and thus we approximate the function by the Taylor series expansion. In this process, we propose four dierent methods of expansion skill.

Keywords

References

  1. Balakrishnan, N. (1989). Approximate MLE of the scale parameter of the Rayleigh distribution with censoring. IEEE Transaction on Reliability, 38, 355-357. https://doi.org/10.1109/24.44181
  2. Caroni, C. (2002). The correct ball bearingdata. Lifetime Data Analysis, 8, 395-399. https://doi.org/10.1023/A:1020523006142
  3. 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
  4. Dyer, D. D. and Whisenand C. W. (1973). Best linear unbiased estimator of the parameter of the Rayleigh distribution. IEEE Transaction on Reliability, 22, 27-34.
  5. Epstein, B. (1954). Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 25, 555-564. https://doi.org/10.1214/aoms/1177728723
  6. Han, J. T. and Kang, S. B. (2006a). Estimation for the Rayleigh distribution with known parameter under multiply Type II censoring. Journal of the Korean Data & Information Science Society, 17, 933-943.
  7. Han, J. T. and Kang, S. B. (2006b). Estimation for two-parameter Rayleigh distribution based on multiply Type II censored sample. Journal of the Korean Data & Information Science Society, 17, 1319-1328.
  8. 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
  9. Kang, S. B. and Jung, W. T. (2009). Estimation for the double Rayleigh distribution based on progressive Type II censored samples. Journal of the Korean Data & Information Science Society, 20, 1199-1206.
  10. Kim, C. and Han, K. (2009). Estimation of the scale parameter of the Rayleigh distribution under general progressive censoring. Journal of the Korean Statistical Society, 38, 239-246. https://doi.org/10.1016/j.jkss.2008.10.005
  11. 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
  12. Lee W. C., Wu J. W., Hong M. L., Lin L. S. and Chan R. L. (2011). Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples. Journal of Computational and Applied Mathematics, 235, 1676-1688. https://doi.org/10.1016/j.cam.2010.09.009
  13. Polovko A. M. (1968). Fundamentals of reliability theory, Academic Press, New York.
  14. Raqab, M. Z. and Wilson, W. M. (2002). Bayesian prediction of the total time on test using doubly censored Rayleigh data. Journal of Statistical Computation and Simulation, 72, 781-789. https://doi.org/10.1080/00949650214670
  15. Rayleigh, J. (1980). On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. Philosophical Magazine, 10, 73-78.
  16. Siddiqui M. M. (1962). Some problems connected with Rayleigh distributions. Journal of Research of the National Bureau of Standards, 60D, 167-174.

Cited by

  1. 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
  2. Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data vol.26, pp.6, 2015, https://doi.org/10.7465/jkdi.2015.26.6.1573
  3. Estimation of entropy of the inverse weibull distribution under generalized progressive hybrid censored data vol.28, pp.3, 2014, https://doi.org/10.7465/jkdi.2017.28.3.659
  4. Bayesian estimation for Rayleigh models vol.28, pp.4, 2014, https://doi.org/10.7465/jkdi.2017.28.4.875