Percentile estimators for the three-parameter weibull distribution for use when all parameters are unknown

Abstract

A new percentile estimator for the scale parameter of the 3-parameter Wei-bull distribution is proposed. This estimator is derived from a class of percentile estimators introduced by Krauth (1992). One of Krauth's percentile estimators for the Weibull shape parameter is shown to be identical to an estimator for the shape parameter due to Zanakis (1979). Dubey (1967b) gave a percentile estimator for the location parameter. We study joint asymptotic properties of Dubey's estimator, Zanakis' estimator and the new estimator for the scale parameter. These (percentile) estimators are compared to efficient estimators for the parameters of the Weibull distribution. Finally, we give numerical results on the asymptotic relative efficiencies of the percentile estimators.

Keywords:

• order statistics
• delta method
• asymptotic normality