Abstract: Simple estimators of the mean are developed and investigated. The Weibull is used as the distributional model for the tail of the observed distribution. No assumption is made about the left portion of the distributions. It is proven that the once-Winsorized mean is superior to the sample mean for Weibull populations with shape parameter greater than one. Estimators for the mean based upon a simple preliminary test for the exponential distribution are illustrated.
Key words and phrases: Skewed distributions, robust estimation, outliers, Weibull, survey sampling.