Simplified Statistical Procedures for the Weibull or Extreme-Value Distribution

REFERENCES

• Abramowitz , M. and Stegun , I. E. 1970 . Handbook of Mathematical Functions Washington , D. C. : National Bureau of Standards. .
   Google Scholar
• Bain , L. J. 1972 . “Inferences based on censored sampling from the Weibull or extreme-value distribution” . Technometrics , 14 : 693 – 702 .
   Web of Science ®Google Scholar
• Billman , B. R. , Antle , C. E. and Bain , L. J. 1972 . “Statistical inferences from censored Weibull samples” . Technomelrics , 14 : 831 – 40 .
   Web of Science ®Google Scholar
• Chernoff , H. , Gastwirth , J. and Johns , M. 1967 . “Asymptotic distribution of linear combinations of order statistics with applications to estimation” . Ann. Math. Statist. , 38 : 52 – 72 .
   Google Scholar
• Engelhardt , M. 1975 . “On simple estimation of the parameters of the Weibull or extreme-value distribution” . Technometrics , 17 : 369 – 74 .
   Web of Science ®Google Scholar
• Engelhardt , M. and Bain , L. J. 1973 . “Some complete and censored sampling results for the Weibull or extreme-value distribution” . Technometrics , 15 : 541 – 9 .
   Web of Science ®Google Scholar
• Engelhardt , M. and Bain , L. J. 1974 . “Some results on point estimation for the two-parameter Weibull or extreme-value distribution” . Technometrics , 16 : 49 – 56 .
   Web of Science ®Google Scholar
• Gray , H. L. , Watk. Ins , T. A. and Adams , J. E. 1972 . “On the jacknife statistic, its extensions, and its relation to en-transformations” . Ann. Math. Statist. , 43 : 1 – 30 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Johns , M. V. and Lieberman , G. J. 1966 . “An exact asymptotically efficient confidence bound for reliability in the case of the Weibull distribution” . Technometrics , 8 : 135 – 75 .
   Web of Science ®Google Scholar
• Lawless , J. F. 1975 . “Construction of tolerance bounds for the extreme-value and Weibull distributions” . Technometrics , 17 : 255 – 61 .
   Web of Science ®Google Scholar
• Lieblein , J. 1953 . “On the exact evaluation of the variances and covariances of order statistics in samples from the extreme-value distribution” . Ann. Math. Statist. , 24 : 282 – 7 .
   Google Scholar
• Mann , N. R. 1968 . Results on statistical estimation and hypothesis testing with applications to the Weibull and extreme-value distributions Wright-Patterson AFB , Ohio : Aerospace Research Labs. . ARL-68–0068
   Google Scholar
• Mann , N. R. 1977 . “An F-approximation for two-parameter Weibull and lognormal tolerance bounds based on possibly censored data, to appear. ” . In Naval Research Logistics Quarterly March 1977
   Google Scholar
• 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 – 101 .
   Web of Science ®Google Scholar
• Mann , N. R. and Fertig , K. W. 1975 . “Simplified efficient point and interval estimators for Weibull parameters” . Technometrics , 17 : 361 – 8 .
   Web of Science ®Google Scholar
• 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 – 93 .
   Web of Science ®Google Scholar
• Mann , N. R. , Fertig , K. W. and Scheuer , E. M. 1971 . “Confidence and tolerance bounds and a new goodness-of-fit test for the two parameter Weibull distributions” Wright-Patterson AFB , Ohio : Office of Aerospace Research. . Aerospace Research Laboratories Report ARL 71–0077
   Google Scholar
• Mann , N. R. and Grubbs , F. E. 1974 . Chi-square approximations for exponential parameters, prediction intervals and beta percentiles” . J. Amer. Statist. Assoc. , 69 : 654 – 661 .
   Web of Science ®Google Scholar
• Mann , N. R. , Schafer , R. E. and Singpurwalla , N. D. 1974 . Methods for Statistical Analysis of Reliability and Life Data New York : John Wiley and Sons. .
   Google Scholar
• McCool , J. I. 1970 . “Inferences on Weibull percentiles and shape parameter from maximum likelihood estimates” . IEEE Transactions on Reliability , R-19 : 2 – 9 .
   Web of Science ®Google Scholar
• McCool , J. I. 1974 . “Inferential techniques for Weibull populations” Wright-Patterson AFT , Ohio : Office of Aerospace Research. . Aerospace Research Laboratories Report ARL TR 74–0180
   Google Scholar
• Thoman , D. R. , Bain , L. J. and Antle , C. E. 1970 . “Maximum likelihood estimation, exact confidence intervals for reliability and tolerance limits in the Weibull distribution” . Technometrics , 12 : 363 – 72 .
   Web of Science ®Google Scholar