A method for computing the circular coverage function

Authors:
A. R. DiDonato and M. P. Jarnagin

Journal:
Math. Comp. **16** (1962), 347-355

MSC:
Primary 62.10

DOI:
https://doi.org/10.1090/S0025-5718-1962-0148161-0

MathSciNet review:
0148161

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References | Similar Articles | Additional Information

**[1]**H. E. Daniels, ``The covering circle of a sample from a circular normal distribution,''*Biometrika*, v. 39, 1952, p. 137-143. MR**0047986 (13:962i)****[2]**N. G. de Bruijn,*Asymptotic Methods in Analysis*, North-Holland Publishing Co., Amsterdam, and Interscience Publishers, Inc., New York, 1958. MR**0099564 (20:6003)****[3]**A. R. DiDonato & M. P. Jarnagin, ``Integration of the general bivariate Gaussian distribution over an offset circle,''*Math. Comp.*, v. 15, 1961, p. 375-382. MR**0129116 (23:B2153)****[4]**A. R. DiDonato & M. P. Jarnagin,*A Method for Computing the Generalized Circular Error Function and the Circular Coverage Function*, NWL Report 1768, U. S. Naval Weapons Laboratory, Dahlgren, Virginia, 23 January 1962.**[5]**R. V. Esperti,*Tables of the Elliptical Normal Probability Function*, Defense Systems Division, General Motors Corporation, Warren, Michigan, 6 April 1960.**[6]**H. E. Fettis,*Some Mathematical Identities and Numerical Methods Relating to the Bivariate Normal Probability for Circular Regions*, WADC Technical Note 57-383, ASTIA Document No. AD142135, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio, December, 1957.**[7]**H. H. Germond,*The Circular Coverage Function*, RAND*Corporation Research Memorandum*RM-330, 26 January 1950.**[8]**A. Gray, G. B. Mathews & T. M. MacRobert,*A Treatise on Bessel Functions and Their Applications to Physics*, Second Edition, The Macmillan Co., New York and London, 1922.**[9]**W. C. Guenther, ``Circular probability problems,''*Amer. Math. Monthly*, v. 68, n. 6, 1961, p. 541-544. MR**1531263****[10]**H. L. Harter, ``Circular error probabilities,''*J. Amer. Statist. Assoc.*, v. 55, n. 292, 1960, p. 723-731. MR**0144403 (26:1948)****[11]**J. R. Lowe, ``A table of the bivariate normal distribution over an offset circle,''*J. Roy. Statist. Soc.*, Ser. B, v. 22, 1960, p. 177-186. MR**0117826 (22:8600)****[12]***Offset Circle Probabilities*, RAND*Corporation Report R*-234, 14 March 1952.**[13]**P. B. Patnaik, ``The non-central - and*F*-distributions and their applications,''*Biometrika*, v. 36, 1949, p. 202-232. MR**0034564 (11:608a)****[14]***Probability-of-Damage Problems of Frequent Occurrence*, OEG*Study*626, Operations Evaluation Group, Office of the Chief of Naval Operations, 11 December 1959.**[15]**H. Ruben, ``Probability content of regions under spherical normal distributions"; I,*Ann. Math. Statist.*, v. 31, 1960, p. 598-618; II, ibid., v. 31, 1960, p. 1113-1121; III, ibid., v. 32, 1961, p. 171-186. MR**0117828 (22:8602)****[16]**H. Solomon,*Distribution of Quadratic Forms-Tables and Applications*, Applied Mathematics and Statistics Laboratories Technical Report No. 45, Stanford University, 5 September 1960.**[17]***Table of Circular Normal Probabilities, Bell Aircraft Corporation Report*#02-949-106, June 1956. Reviewed in MTAC, v. 11, 1957, p. 210.**[18]**H. Weingarten & A. R. DiDonato, ``A table of generalized circular error,''*Math. Comp.*, v. 15, 1961, p. 169-173. MR**0127563 (23:B608)**

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DOI:
https://doi.org/10.1090/S0025-5718-1962-0148161-0

Article copyright:
© Copyright 1962
American Mathematical Society