A method for computing the circular coverage function
Authors:
A. R. DiDonato and M. P. Jarnagin
Journal:
Math. Comp. 16 (1962), 347355
MSC:
Primary 62.10
MathSciNet review:
0148161
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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H.
E. Daniels, The covering circle of a sample from a circular normal
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(13,962i)
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R. DiDonato and M.
P. Jarnagin, Integration of the general bivariate
Gaussian distribution over an offset circle, Math. Comp. 15 (1961), 375–382. MR 0129116
(23 #B2153), http://dx.doi.org/10.1090/S00255718196101291168
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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.
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R. V. Esperti, Tables of the Elliptical Normal Probability Function, Defense Systems Division, General Motors Corporation, Warren, Michigan, 6 April 1960.
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H. E. Fettis, Some Mathematical Identities and Numerical Methods Relating to the Bivariate Normal Probability for Circular Regions, WADC Technical Note 57383, ASTIA Document No. AD142135, Wright Air Development Center, WrightPatterson Air Force Base, Ohio, December, 1957.
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H. H. Germond, The Circular Coverage Function, RAND Corporation Research Memorandum RM330, 26 January 1950.
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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.
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Monthly 68 (1961), no. 6, 541–544. MR
1531263, http://dx.doi.org/10.2307/2311145
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Leon Harter, Circular error probabilities, J. Amer. Statist.
Assoc. 55 (1960), 723–731. MR 0144403
(26 #1948)
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R. Lowe, A table of the integral of the bivariate normal
distribution over an offset circle, J. Roy. Statist. Soc. Ser. B
22 (1960), 177–187. MR 0117826
(22 #8600)
 [12]
Offset Circle Probabilities, RAND Corporation Report R234, 14 March 1952.
 [13]
P.
B. Patnaik, The noncentral 𝜒² and
𝐹distributions and their applications, Biometrika
36 (1949), 202–232. MR 0034564
(11,608a)
 [14]
ProbabilityofDamage Problems of Frequent Occurrence, OEG Study 626, Operations Evaluation Group, Office of the Chief of Naval Operations, 11 December 1959.
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Harold
Ruben, Probability content of regions under spherical normal
distributions. I., Ann. Math. Statist. 31 (1960),
598–618. MR 0117828
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H. Solomon, Distribution of Quadratic FormsTables 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 #02949106, June 1956. Reviewed in MTAC, v. 11, 1957, p. 210.
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Harry
Weingarten and A.
R. DiDonato, A table of generalized circular
error, Math. Comp. 15 (1961), 169–173. MR 0127563
(23 #B608), http://dx.doi.org/10.1090/S00255718196101275631
 [1]
 H. E. Daniels, ``The covering circle of a sample from a circular normal distribution,'' Biometrika, v. 39, 1952, p. 137143. MR 0047986 (13:962i)
 [2]
 N. G. de Bruijn, Asymptotic Methods in Analysis, NorthHolland 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. 375382. 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 57383, ASTIA Document No. AD142135, Wright Air Development Center, WrightPatterson Air Force Base, Ohio, December, 1957.
 [7]
 H. H. Germond, The Circular Coverage Function, RAND Corporation Research Memorandum RM330, 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. 541544. MR 1531263
 [10]
 H. L. Harter, ``Circular error probabilities,'' J. Amer. Statist. Assoc., v. 55, n. 292, 1960, p. 723731. 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. 177186. MR 0117826 (22:8600)
 [12]
 Offset Circle Probabilities, RAND Corporation Report R234, 14 March 1952.
 [13]
 P. B. Patnaik, ``The noncentral  and Fdistributions and their applications,'' Biometrika, v. 36, 1949, p. 202232. MR 0034564 (11:608a)
 [14]
 ProbabilityofDamage 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. 598618; II, ibid., v. 31, 1960, p. 11131121; III, ibid., v. 32, 1961, p. 171186. MR 0117828 (22:8602)
 [16]
 H. Solomon, Distribution of Quadratic FormsTables 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 #02949106, 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. 169173. MR 0127563 (23:B608)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196201481610
PII:
S 00255718(1962)01481610
Article copyright:
© Copyright 1962
American Mathematical Society
