A geometric confidence ellipse approach to the estimation of the ratio of two variables

One is often interested in the ratio of two variables, for example in genetics, assessing drug effectiveness, and in health economics. In this paper, we derive an explicit geometric solution to the general problem of identifying the two tangents from an arbitrary external point to an ellipse. This solution permits numerical integration of a bivariate normal distribution over a wedge-shaped region bounded by the tangents, which yields an …