A uniform approximation to the sampling distribution of the coefficient of variation

According to Hendricks and Robey (1936) the coefficient of variation from a normal population with sample size n can be approximated by a function defined on the positive real line, which depends on the standard normal moment of order n - 1 about some well-defined point. Simple conditions under which this approximation is valid are derived. It is shown that the approximation error depends upon a standard normal stop-loss moment of order n - 1 about some point. As a main result we obtain a uniform error bound to the exact sampling density of the order of magnitude exp (- n/2k2), where k is the coefficient of variation.