Confidence Intervals for a Normal Coefficient of Variation

Abstract

Abstract This article presents an analysis of the small-sample distribution of a class of approximate pivotal quantities for a normal coefficient of variation that contains the approximations of McKay, David, the “naïve” approximate interval obtained by dividing the usual confidence interval on the standard deviation by the sample mean, and a new interval closely related to McKay. For any approximation in this class, a series is given for e(t) the difference between the cdf's of the approximate pivot and the reference distribution. Let κ denote the population coefficient of variation. For McKay, David, and the “naïve” interval e(t) = O(κ2), while for the new procedure e(t) = O(κ4).