Confidence intervals for the ratio of two means using the distribution of the quotient of two normals

In various scientific fields, such as medicine, biology and bioassay, several ratio quantities, assumed to be Normal, are of potential interest. The estimator of the ratio of two means is a ratio of two random variables normally or asymptotically normally distributed. The present paper shows the importance of considering the real distribution of the estimator of the ratio of two means, because generally the approximation to Normal is not satisfied. The estimated of the asymptotic cumulative and density function of the estimator of the ratio is presented, with several consideration on the skewness. Finally, a new method for the building of confidences intervals for the ratio of two means was proposed. Differently from other parametric methods, this new method is preferable because it consider the skewness in the distribution of the ratio estimator and the confidence intervals are always bounded.