Abstract
A percentile estimator for the shape parameter of the Weibull distribution, based on the 17th and 97th sample percentiles, is proposed which is asymptotically about 66% efficient when compared with the MLE (maximum likelihood estimator). A two-observation percentile estimator, based on the 40th and 82nd sample percentiles, for the scale parameter when the shape parameter is unknown is asymptotically about 82y0 efficient when compared with the MLE. The 24th and 93rd sample percentiles yield asymptotically about 41ye jointly efficient percentile estimators for both the scale and shape parameters in a class of two-observation percentile estimators when compared with their MLEs. Some other simple percentile estimators for these parameters are also briefly discussed. Finally, asymptotic properties of these estimators are investigated and their application in statistical inference problems is mentioned.
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