A note on circular error probabilities

Z. Govindarajulu

Naval Research Logistics Quarterly, 1986, vol. 33, issue 3, 423-429

Abstract: An approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2.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.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:33:y:1986:i:3:p:423-429

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