DOI QR코드

DOI QR Code

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

Kim Chan-Soo

  • Published : 2006.04.01

Abstract

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.

Keywords

Burr Type XII distribution;General progressive Type II censoring;HPD credible interval;Linex loss

References

  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. Cohen, A.C. (1963). Progressively censored samples In life testing. Technometrics, Vol. 5, 327-339 https://doi.org/10.2307/1266337
  5. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos de Stadistca, Vol. 21, 223-237
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. Burr, IW. (1942). Cumulative frequency functions. Annals of Mathematics, Vol. 43, 1441-1449

Cited by

  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