Distribution of the normal scores estimator of the standard deviation of a normal population

Abstract

SUMMARY The normal scores estimator of the standard deviation of a normal population is an easily obtained unbiased nearly best linear estimator. Its distribution, although difficult to derive explicitly, is shown to be closely approximated by the distribution of cX v /√v , where X v has a X distribution with v degrees of freedom and c is a scale factor. Exact or approximate values of the parameters c and v are determined which allow the usual tests of significance for the population parameters to be carried out using existing tables of percentage points.