Moment series for moment estimators of the parameters of a Weibull density

Abstract

Taylor series for the first four moments of the coefficients of variation in sampling from a 2-parameter Weibull density are given: they are taken as far as the coefficient of n/sup -24/. From these a four moment approximating distribution is set up using summatory techniques on the series. The shape parameter is treated in a similar way, but here the moment equations are no longer explicit estimators, and terms only as far as those in n/sup -12/ are given. The validity of assessed moments and percentiles of the approximating distributions is studied. Consideration is also given to properties of the moment estimator for 1/c