Simplified Efficient Point and Interval Estimators for Weibull Parameters

In this paper are tabulated values which allow one to obtain, without lengthy tables of weights, simplified linear estimates of Weibull or extreme-value distribution parameters which approximate best linear invariant, best linear unbiased, or maximumlikelihood estimates. Asymptotic distributional results proved herein, together with these tabulated values, make it possible to obtain confidence bounds for both parameters from censored or uncensored samples of size n, with n = 20(5)60. Other tabulations and related results are given by Bain (1972) and Engelhardt, and Bain (1973, 1974).

[1]  Julius Lieblein,et al.  On the Exact Evaluation of the Variances and Covariances of Order Statistics in Samples from the Extreme-Value Distribution , 1953 .

[2]  J. Lieblein,et al.  Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings , 1956 .

[3]  N. Mann,et al.  A men goodness-of-fit test for the two-parameter wetbull or extreme-value distribution with unknown parameters , 1973 .

[4]  Bradford F. Kimball THE BIAS IN CERTAIN ESTIMATES OF THE PARAMETERS OF THE EXTREME-VALUE DISTRIBUTION , 1956 .

[5]  Nancy R. Mann,et al.  Tables for Obtaining Weibull Confidence Bounds and Tolerance Bounds Based on Best Linear Invariant Estimates of Parameters of the Extreme-Value Distribution , 1973 .

[6]  P. Patnaik THE NON-CENTRAL χ2- AND F-DISTRIBUTIONS AND THEIR APPLICATIONS , 1949 .

[7]  Nancy R. Mann,et al.  Tables for Obtaining the Best Linear Invariant Estimates of Parameters of the Weibull Distribution , 1967 .

[8]  Lee J. Bain,et al.  Some Complete and Censored Sampling Results for the Weibull or Extreme-Value Distribution , 1973 .

[9]  F. Mosteller On Some Useful "Inefficient" Statistics , 1946 .

[10]  Nancy R. Mann,et al.  Approximately Optimum Confidence Bounds on Series- and Parallel-system Reliability for Systems with Binomial Subsystem Data , 1974 .

[11]  L. J. Bain Inferences Based on Censored Sampling From the Weibull or Extreme-Value Distribution , 1972 .

[12]  A Note on WilsonHilferty Transformation of χ2 , 1961 .

[13]  Albert H. Moore,et al.  Maximum-Likelihood Estimation, from Doubly Censored Samples, of the Parameters of the First Asymptotic Distribution of Extreme Values , 1968 .

[14]  Charles E. Antle,et al.  Statistical Inference From Censored Weihull Samples , 1972 .

[15]  N. Mann Point and Interval Estimation Procedures for the Two-Parameter Weibull and Extreme-Value Distributions , 1968 .

[16]  L. J. Bain,et al.  Some Results on Point Estimation for the Two-Parameter Weibull or Extreme-Value Distribution , 1974 .

[17]  Frank E. Grubbs,et al.  Approximately optimum confidence bounds on series system reliability for exponential time to failure data , 1972 .

[18]  E. B. Wilson,et al.  The Distribution of Chi-Square. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Frank E. Grubbs,et al.  Approximate Fiducial Bounds for the Reliability of a Series System for Which Each Component has an Exponential Time-to-Fail Distribution , 1971 .

[20]  Frank E. Grubbs,et al.  Approximate Circular and Noncircular Offset Probabilities of Hitting , 1964 .

[21]  S. S. Wilks Determination of Sample Sizes for Setting Tolerance Limits , 1941 .

[22]  M.A.J. Van Montfort,et al.  On testing that the distribution of extremes is of type I when type II is the alternative , 1970 .

[23]  J. Lawless Conditional versus Unconditional Confidence Intervals for the Parameters of the Weibull Distribution , 1973 .

[24]  L. K. Chan,et al.  Optimum quantiles for the linear estimation of the parameters of the extreme value distribution in complete and censored samples , 1969 .

[25]  Nancy R. Mann,et al.  Optimum Estimators for Linear Functions of Location and Scale Parameters , 1969 .

[26]  Khatab M. Hassanein,et al.  Simultaneous Estimation of the Parameters of the Extreme Value Distribution by Sample Quantiles , 1972 .

[27]  N. Mann RESULTS ON LOCATION AND SCALE PARAMETER ESTIMATION WITH APPLICATION TO THE EXTREME-VALUE DISTRIBUTION , 1967 .