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 Free Access

References | Similar Articles | Additional Information

**[1]**H. E. Daniels,*The covering circle of a sample from a circular normal distribution*, Biometrika**39**(1952), 137–143. MR**0047986**, https://doi.org/10.1093/biomet/39.1-2.137**[2]**N. G. de Bruijn,*Asymptotic methods in analysis*, Bibliotheca Mathematica. Vol. 4, North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen; Interscience Publishers Inc., New York, 1958. MR**0099564****[3]**A. 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**, https://doi.org/10.1090/S0025-5718-1961-0129116-8**[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]**William C. Guenther,*Circular Probability Problems*, Amer. Math. Monthly**68**(1961), no. 6, 541–544. MR**1531263**, https://doi.org/10.2307/2311145**[10]**H. Leon Harter,*Circular error probabilities*, J. Amer. Statist. Assoc.**55**(1960), 723–731. MR**0144403****[11]**J. 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****[12]***Offset Circle Probabilities*, RAND*Corporation Report R*-234, 14 March 1952.**[13]**P. B. Patnaik,*The non-central 𝜒² and 𝐹-distributions and their applications*, Biometrika**36**(1949), 202–232. MR**0034564****[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]**Harold Ruben,*Probability content of regions under spherical normal distributions. I.*, Ann. Math. Statist.**31**(1960), 598–618. MR**0117828**, https://doi.org/10.1214/aoms/1177705788**[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]**Harry Weingarten and A. R. DiDonato,*A table of generalized circular error*, Math. Comp.**15**(1961), 169–173. MR**0127563**, https://doi.org/10.1090/S0025-5718-1961-0127563-1

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

Article copyright:
© Copyright 1962
American Mathematical Society