Some characteristics of the estimator of the ratio of two means

Generally only the asymptotic expectation and the asymptotic variance of the estimator of the ratio of two means are considered. In the present paper, the estimate of the asymptotic density function of the estimator of the ratio is presented. In fact, in different situations having the same asymptotic expectation and variance of the estimator, the density function may differ in a considerably way especially with respect to the skewness. Confidence intervals for the ratio of two means which keep in consideration the shape of the distribution, proposed by Galeone, are reported.