Small sample asymptotic inference for the coefficient of variation: normal and nonnormal models

In applied statistics, the coefficient of variation is widely calculated and interpreted even when the sample size of the data set is very small. However, confidence intervals for the coefficient of variation are rarely reported. One of the reasons is the exact confidence interval for the coefficient of variation, which is given in Lehmann (Testing Statistical Hypotheses, 2nd Edition, Wiley, New York, 1996), is very difficult to calculate. Various asymptotic methods have been proposed in literature. These methods, in general, require the sample size to be large. In this article, we will apply a recently developed small sample asymptotic method to obtain approximate confidence intervals for the coefficient of variation for both normal and nonnormal models. These small sample asymptotic methods are very accurate even for very small sample size. Numerical examples are given to illustrate the accuracy of the proposed method.