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Article

Linear Bayes estimator of the extreme value distribution based on type II censored samples

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Pages 4532-4544 | Received 23 Apr 2021, Accepted 28 Jul 2021, Published online: 09 Sep 2021

References

  • Al-Aboud, F. M. 2009. Bayesian estimations for the extreme value distribution using progressive censored data and asymmetric loss. International Mathematical Forum 4:1603–22.
  • Bain, L. J. 1972. Inferences based on censored sampling from the Weibull or extreme-value distribution. Technometrics 14 (3):693–702. doi:10.1080/00401706.1972.10488958.
  • Balakrishnan, N., and P. S. Chan. 1992. Order statistics from extreme value distribution, II: Best linear unbiased estimates and some other uses. Communications in Statistics - Simulation and Computation 21 (4):1219–46. doi:10.1080/03610919208813074.
  • Balakrishnan, N., and J. Varadan. 1991. Approximate mles for the location and scale parameters of the extreme value distribution with censoring. IEEE Transactions on Reliability 40 (2):146–51. doi:10.1109/24.87115.
  • Chernoff, H., J. L., Gastwirth, and M. V. Johns. 1967. Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation. The Annals of Mathematical Statistics 38 (1):52–72. doi:10.1214/aoms/1177699058.
  • D’agostino, R. B. 1971. Linear estimation of the Weibull parameters. Technometrics 13 (1):171–82.
  • Engelhardt, M., and L. J. Bain. 1974. Some results on point estimation for the two-parameter Weibull or extreme-value distribution. Technometrics 16 (1):49–56. doi:10.1080/00401706.1974.10489148.
  • Harter, H. L., and A. H. Moore. 1968. Maximum-likelihood estimation from doubly censored samples of the parameters of the first asymptotic distribution of extreme values. Journal of the American Statistical Association 63 (323):889–901. doi:10.2307/2283881.
  • Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1):97–109. doi:10.1093/biomet/57.1.97.
  • LaMotte, L. R. 1978. Bayes linear estimators. Technometrics 20 (3):281–90. doi:10.1080/00401706.1978.10489673.
  • Lawless, J. F. 1982. Statistical models and methods for lifetime data. New York: John Wiley & Sons.
  • Lindley, D. V. 1980. Approximate Bayesian methods. Trabajos de Estadistica Y de Investigacion Operativa 31 (1):223–45. doi:10.1007/BF02888353.
  • Mann, N. R. 1967. Tables for obtaining the best linear invariant estimates of parameters of the Weibull distribution. Technometrics 9 (4):629–45. doi:10.1080/00401706.1967.10490511.
  • Mann, N. R., and K. W. Fertig. 1973. Tables for obtaining Weibull confidence bounds and tolerance bounds based on best linear invariant estimates of parameters of the extreme-value distribution. Technometrics 15 (1):87–101. doi:10.1080/00401706.1973.10489013.
  • Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equation of state calculations by fast computing machines. The Journal of Chemical Physics 21 (6):1087–92. doi:10.1063/1.1699114.
  • Rao, C. R. 1973. Linear statistical inference and its applications. Vol. 2. New York: Wiley.
  • Samaniego, F. J., and E. Vestrup. 1999. On improving standard estimators via linear empirical Bayes methods. Statistics & Probability Letters 44 (3):309–18. doi:10.1016/S0167-7152(99)00022-X.
  • Tierney, L., and J. B. Kadane. 1986. Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association 81 (393):82–86. doi:10.1080/01621459.1986.10478240.
  • Wang, L. 2015. How to improve classical estimators via linear Bayes method? Communications for Statistical Applications and Methods 22 (6):531–42. doi:10.5351/CSAM.2015.22.6.531.
  • Wang, L., and R. S. Singh. 2014. Linear Bayes estimator for the two-parameter exponential family under type II censoring. Computational Statistics & Data Analysis 71:633–42. doi:10.1016/j.csda.2013.07.020.
  • Wei, L., and W. Zhang. 2007. The superiorities of Bayes linear minimum risk estimation in linear model. Communications in Statistics - Theory and Methods 36 (5):917–26. doi:10.1080/03610920601036333.
  • White, J. S. 1969. The moments of log-Weibull order statistics. Technometrics 11 (2):373–86. doi:10.1080/00401706.1969.10490691.

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