## Quick Reference

A theorem first stated by E. C. Fieller in 1940. Suppose that the random variables *X* and *Y* have means *μ** _{x}* and

*μ*

*, respectively, and a bivariate normal distribution. The quantity of interest is*

_{y}*γ*, the ratio of the two means:. Let

*x̄*and

*x̄*be estimates of

*μ*

*and*

_{x}*μ*

*, respectively, and let the respective estimates of the variances and covariance be denoted by*

_{y}*s*

_{x}^{2},

*s*

_{y}^{2}and

*c*

*, with*

_{xy}*ν*degrees of freedom. Fieller's theorem states that has a

*t*-distribution with

*ν*degrees of freedom.

*Subjects:*
Probability and Statistics.