A theorem first stated by E. C. Fieller in 1940. Suppose that the random variables X and Y have means μx and μy , respectively, and a bivariate normal distribution. The quantity of interest is γ, the ratio of the two means:. Let x̄ and x̄ be estimates of μx and μy, respectively, and let the respective estimates of the variances and covariance be denoted by sx2, sy2 and cxy, with ν degrees of freedom. Fieller's theorem states that has a t-distribution with ν degrees of freedom.
Subjects: Probability and Statistics.