Point and Interval Estimation Procedures for the Two-Parameter Weibull and Extreme-Value Distributions

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Abstract
Point estimators of parameters of the first asymptotic distribution of smallest (extreme) values, or, the extreme-value distribution, are surveyed and compared. Those investigated are maximum-likelihood and moment estimators, inefficient estimators based on only a few ordered observations, and various linear estimation methods. A combination of Monte Carlo approximations and exact small-sample and asymptotic results has been used to compare the expected loss (with loss equal to squared error) of these various point estimators. Since the logarithms of variates having the two-parameter Weibull distribution are variates from the extreme-value distribution, the investigation is applicable to the estimation of Weibull parameters. Interval estimation procedures are also discussed.

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