Computation of the bivariate normal integral

Author:
Z. Drezner

Journal:
Math. Comp. **32** (1978), 277-279

MSC:
Primary 65D20; Secondary 33A20

MathSciNet review:
0461849

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Abstract: This paper presents a simple and efficient computation for the bivariate normal integral based on direct computation of the double integral by the Gauss quadrature method.

**[1]**Norman L. Johnson and Samuel Kotz,*Distributions in statistics: continuous multivariate distributions*, John Wiley & Sons, Inc., New York-London-Sydney, 1972. Wiley Series in Probability and Mathematical Statistics. MR**0418337****[2]**A. H. Stroud and Don Secrest,*Gaussian quadrature formulas*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR**0202312****[3]**N. M. Steen, G. D. Byrne, and E. M. Gelbard,*Gaussian quadratures for the integrals ₀^{∞}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥 and ₀^{𝑏}𝑒𝑥𝑝(-𝑥²)𝑓(𝑥)𝑑𝑥*, Math. Comp.**23**(1969), 661–671. MR**0247744**, 10.1090/S0025-5718-1969-0247744-3**[4]**R. R. Sowden and J. R. Ashford,*Computation of the bi-variate normal integral*, J. Roy. Statist. Soc. Ser. C Appl. Statist.**18**(1969), 169–180. MR**0247690****[5]**D. E. Amos,*On computation of the bivariate normal distribution*, Math. Comp.**23**(1969), 655–659. MR**0247733**, 10.1090/S0025-5718-1969-0247733-9**[6]**Yudell L. Luke,*Mathematical functions and their approximations*, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0501762**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0461849-9

Article copyright:
© Copyright 1978
American Mathematical Society