| Abstract: | An approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2. Also, we provide asymptotic expressions for the probabilities for large values of β = K2(1 - c2)/4c2 where c = σ2/σ1. These are illustrated by comparing with values tabulated by Harter 6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals. |
