We consider the problem of finding $\alpha$-level confidence intervals for the ratio of two normally estimated means. We show that there is no procedure that with probability 1 gives bounded $\alpha$-level confidence intervals for the ratio, and we show that within a large class of sensible procedures the Fieller solution is the only one with exact coverage probability.
"A Characterization of the Fieller Solution." Ann. Statist. 15 (1) 462 - 468, March, 1987. https://doi.org/10.1214/aos/1176350282