Communications for Statistical Applications and Methods

  • 제13권1호
  • /
  • Pages.89-99
  • /
  • 2006
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

On Estimating Burr Type XII Parameter Based on General Type II Progressive Censoring

  • Kim Chan-Soo (Department of Applied Mathematics, Kongju National University)
  • 발행 : 2006.04.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

키워드

참고문헌

  1. Aggarwala, R. and Balakrishnan, N. (1998). Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. Journal of Statistical Planning and Inference, Vol. 70, 35-49 https://doi.org/10.1016/S0378-3758(97)00173-0
  2. Balakrishnan, N. and Aggarwala, R. (2000). Progressive censoring: Theory, Methods, and Applications. Boston, MA: Birkhauser
  3. Balakrishnan, N. and Sandhu, R.A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples. Sankhya B, Vol. 58, 1-9
  4. Burr, IW. (1942). Cumulative frequency functions. Annals of Mathematics, Vol. 43, 1441-1449
  5. Cohen, A.C. (1963). Progressively censored samples In life testing. Technometrics, Vol. 5, 327-339 https://doi.org/10.2307/1266337
  6. Fernandez, A.J. (2004). On estimating exponential parameters with general type II progressive censoring. Journal of Statistical Planning and Inference, Vol. 121, 135-147 https://doi.org/10.1016/S0378-3758(03)00083-1
  7. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos de Stadistca, Vol. 21, 223-237
  8. Mann, N.R. (1971). Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics, Vol. 13, 521-533 https://doi.org/10.2307/1267165
  9. Thomas, D.R. and Wilson, W.M. (1972). Linear order statistic estimation for the two parameter Weibull and extreme-value distribution under Type II progressively censored samples. Technometrics, Vol. 14, 679-691 https://doi.org/10.2307/1267296
  10. Tierney, L. and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association. Vol. 81, 82-86 https://doi.org/10.2307/2287970
  11. Viveros, R. and Balakrishnan, N. (1994). Interval estimation of life characteristics from progressively censored samples. Technometrics, Vol. 36, 84-91 https://doi.org/10.2307/1269201
  12. Varian, H. (1975). A Bayesian approach to real estate assessment, in Fienber S.E., Zellner A. (Eds.), Studies in Bayesian Econometrics and Statistics in honour of Leonard J. Savage, North-Holland, Amsterdam, 195-208
  13. Zellner, A. (1986) Bayesian estimation and prediction using asymmetric loss function. Journal of the American Statistical Association, Vol. 81, 446-451 https://doi.org/10.2307/2289234

피인용 문헌

  1. Predicting observables from Weibull model based on general progressive censored data with asymmetric loss vol.8, pp.5, 2011, https://doi.org/10.1016/j.stamet.2011.05.003