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Original Articles

Estimation of the location and scale parameters of the extreme value distmbution based on multiply type-II censored samples

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Pages 2105-2125 | Received 01 Feb 1995, Published online: 27 Jun 2007

References

  • Arnold , B.C. and Balakrishnan , N. 1989 . “ Lecture Notes in Statistics No. 53 ” . In Relations, Bounds and Approximations for Order Statistics , New York : Springer-Verlag .
  • Balakrishnan , N. and Chan , P. S. 1992 a . Order statistics from extreme value distribution, I: Tables of means, variances and covariances . Communications in Statistics - Theory and Methods , 21 ( 4 ) : 1199 – 1217 .
  • Balakrishnan , N. and Chan , P. S. 1992 b . Order statistics from extreme value distribution, II: Best linear unbiased estimates and some other uses . Communications in Statistics - Theory and Methods , 21 ( 4 ) : 1219 – 1246 .
  • Balakrishnan , N. and Cohen , A.C. 1991 . Order Statistics and Inference: Estimation Methods , San Diego : Academic Press .
  • Balakrishnan , N. and Varadan , J. 1991 . Approximate MLEs for the location and scale parameters of the extreme value distribution with censoring . IEEE Trans. on Reliab. , R-40 : 146 – 151 .
  • Chan , L.K. and Kabir , A.B.M.L. 1969 . Optimum quantiles for the linear estimation of the parameters of the extreme-value distribution in complete and censored samples . Naval Res. Logist. Quart. , 16 : 381 – 404 .
  • Chan , L. K. and Mead , E. R. 1971 . Linear estimation of the parameters of the extreme-value distribution based on suitably chosen order statistics . IEEE Trans. on Reliab. , R-20 : 74 – 83 .
  • D’ Agostino , R.B. 1971 . Linear estimation of the Weibull parameters . Technometrics , 13 : 171 – 182 .
  • David , F.N. and Johnson , N.L. 1954 . Statistical treatment of censored data. I. Fundamental formulae . Biomeirika , 41 : 228 – 240 .
  • David , H.A. 1981 . Order Statistics , second edition , New York : John Wiley & Sons .
  • Engelhardt , M. and Bain , L.J. 1977 . Simplified statistical procedures for the Weibull or extreme value distribution . Technometrics , 19 : 323 – 331 .
  • Harter , H.L. 1970 . Order Statistics and their Use in Testing and Estimation , Vol. 2 , Washington, D. C : U.S. Govt. Printing Office .
  • Harter , H.L. and Moore , A.H. 1968 . Maximum-likelihood estimation, from doubly censored samples, of the parameters of the first asymptotic distribution of extreme values . J. Amer. Statist. Assoc. , 63 : 889 – 901 .
  • Hassandn , K.M. 1968 . Analysis of extreme value data by sample quantiles for very large samples . J. Amer. Statist. Assoc. , 61 : 852 – 855 .
  • Hassanein , K.M. 1969 . Estimation of the parameters of the extreme value distribution by use of two or three order statistics . Biometrika , 56 : 429 – 436 .
  • Hassanein , K.M. 1972 . Simultaneous estimation of the parameters of the extreme value distribution by sample quantiles . Technometrics , 14 : 63 – 70 .
  • Hassanein , K.M. , Saleh , h. A.K. Md. E. and Brown , E.F. 1984 . Quantile estimates in complete and censored samples from extreme-value and Weibull distributions . IEEE Trans. on Reliab. , R-33 : 370 – 373 .
  • Hassanein , K.M. , Saleh , A.K. Md. E. and Brown , E. F. 1986 . Estimation and testing of quantiles of the extreme-value distribution . J. Statist. Plann. Inf. , 14 : 389 – 400 .
  • Kendall , M.G. and Stuart , A. 1973 . The Advanced Theory of Statistics , Vol. 2 , London : Charles Griffin and Co. .
  • Lawless , J. F. 1982 . Statistical Modeb & Methods For Lifetime Data , New York : John Wiley & Sons .
  • Lieblein , J. and Salzer , H.E. 1957 . Table of the first moment of ranked extremes . J. Res. Nat. Bur. Stand. , 59 : 203 – 206 .
  • Lieblein , J. and Zelen , M. 1956 . Statistical investigation of the fatigue life of deep-grove ball bearings . J. Res. Nat. Bur. Stand. , 57 : 273 – 316 .
  • Lloyd , E. H. 1952 . Least squares estimation of location and scale parameters using order statistics . Biometrika , 39 : 88 – 95 .
  • Mann , N. R. 1967a . Tables for obtaining the best linear invariant estimates of parameters of the Weibull distribution . Technometrics , 9 : 629 – 645 .
  • Mann , N. . Results on location and scale parameter estimation with application to the extreme-value distribution . Technical Report No. 28 . Ohio : Aerospace Research Laboratories, Wright-Patterson AFB .
  • Mann , N. R. 1968 . Point and interval estimation procedures for the two-parameter Weibull and extreme-value distributions . Technometrics , 10 : 231 – 256 .
  • Mann , N. R. and Fertig , K. W. 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 : 87 – 102 .
  • Mann , N. R. and Fertig , K. W. 1977 . Efficient unbiased quantile estimators for moderate-size complete samples from extreme-value and Weibull distributions: confidence bounds and tolerance and prediction intervals . Technometrics , 19 : 87 – 94 .
  • Mann , N. R. , Schafer , R. E. and Singpurwalla , N.D. 1974 . Methods for Statistical Analysis of Reliability and Life Data , New York : John Wiley & Sons .
  • Rao , C. R. 1975 . Linear Statistical Inference and Its Applications , New York : John Wiley & Sons .
  • Tiku , M. L. , Tan , W. Y. and Balakrishnan , N. 1986 . Robust Inference , New York : Marcel Dekker .
  • White , J. S. 1969 . The moments of log-Weibull order statistics . Technometrics , 11 : 373 – 386 .

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