{"title":"A note on circular error probabilities","authors":"Z. Govindarajulu","doi":"10.1002/NAV.3800330308","DOIUrl":null,"url":null,"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approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2.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.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"97 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Naval Research Logistics Quarterly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/NAV.3800330308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
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An approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2.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.
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