Abstract
Simple estimators of the Weibull shape parameter and any quantile in uncensored samples are shown to share the pivotal function properties of maximum likelihood estimators. This allows interval estimation of the Weibull parameters and quantiles once the distributions of the necessary pivotal functions are determined by Monte Carlo sampling for a given sample size and quantile of interest. Free software for this purpose is made available for download. It is shown that the quantile and shape parameter estimates may be readily corrected so as to be median unbiased. The shape parameter estimator is shown to be less precise than the corresponding maximum likelihood estimator. However, the precision of the estimator of the pth quantile is quite comparable to that of the maximum likelihood method over the range from 0.4≤ p≤0.7.
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