Analytical derivation of an accurate approximation of CEP for elliptical error distributions

A very simple, closed-form approximation to circular error probable (CEP) is determined analytically for the case when the underlying error distribution is elliptical. The accuracy of the approximation is quite good over a sizeable range of major-to-minor axis ratios. Accurate numerical CEP computations are shown, but for many applications only the approximation will be required. The inverse question of what percentage of elliptically distributed points lie within a circle of given radius is also considered.