Integration of the general bivariate Gaussian distribution over an offset circle

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

Journal:
Math. Comp. **15** (1961), 375-382

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1961-0129116-8

MathSciNet review:
0129116

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References | Similar Articles | Additional Information

**[1]**A. R. DiDonato & M. P. Jarnagin,*Integration of the General Bivariate Gaussian Distribution over an Offset Ellipse*, NWL Report 1710, U. S. Naval Weapons Laboratory, Dahlgren, Virginia, 11 August 1960, unclassified.**[2]**H. H. Germond,*Integration of the Gaussian Distribution over an Offset Ellipse*, RAND Corporation Report No. P-94, 28 July 1949, unclassified.**[3]**J. R. Lowe,*Integration of the Binormal Distribution over an Offset Circle*, ARDE Memorandum (B) 5/60, Armament Research and Development Establishment, Fort Halstead, Kent, England, February 1960, unclassified.**[4]**OEG Study 626,*Probability-of-Damage Problems of Frequent Occurrence*, Operations Evaluation Group, Office of the Chief of Naval Operations, 11 December 1959, unclassified.**[5]**P. C. Hammer, ``Numerical evaluation of multiple integrals,''*On Numerical Approximation*, University of Wisconsin Press, Madison, Wisconsin, 1959, p. 99-115. MR**0100355 (20:6788)****[6]**W. H. Peirce, ``Numerical integration over the planar annulus,''*J. Soc Indust. Appl. Math.*, v. 5, 1957, p. 66-73. MR**0090122 (19:771b)****[7]**(a) P. Davis & P. Rabinowitz, ``Abscissae and weights for Gaussian quadratures of high order,''*J. Res. Nat. Bur. Standards*, v. 56, January 1956, p. 35 (for orders 20, 24). (b) A. N. Lowan, N. Davids, & A. Levenson, ``Table of the zeros of the Legendre polynomials of order 1-16 and the weight coefficients for Gauss' mechanical quadrature formula,'' p. 185-189 of*Tables of Functions and of Zeros of Functions, Nat. Bur. Standards Appl. Math. Ser.*, No. 37, U. S. Government Printing Office, Washington, D.C., 1954 (for orders 6, 8, 12, 16) MR**0076463 (17:902g)****[8]**Nat. Bur. Standards Appl. Math. Ser. No. 41,*Tables of the Error Function and its Derivative*, U. S. Government Printing Office, Washington, D. C, 1954.

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DOI:
https://doi.org/10.1090/S0025-5718-1961-0129116-8

Article copyright:
© Copyright 1961
American Mathematical Society