Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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 $ {\chi ^2}$- 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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 62.10

Retrieve articles in all journals with MSC: 62.10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1962-0148161-0
Article copyright: © Copyright 1962 American Mathematical Society

American Mathematical Society