Computing Probability Integrals of a Bivariate Normal Distribution

by Saeed Maghsoodloo and Chien-Lung Huang.

Abstract: The bivariate normal integral has been computed and tabulated in several sources in thepast 40 years. The objective of this paper is two-fold. First, matrix algebra and geometry is usedto reduce the complexity of evaluating the normal double integral thru a transformation to asingle integral of the cumulative univariate standardized normal distribution. As a result, theaccuracy for the volume under the bivariate normal density is at least through 7 decimals.Secondly, the objective is to present a very user-friendly software that computes the volume overboth elliptical and rectangular regions. The user may specify the level of accuracy by inputtingthe number of subintervals for the Simpson's Rule.

Key Words: Bivariate Normal Integral, Matrix Transformation, Computer Software

Saeed Maghsoodloo,
Chien-Lung Huang

Editor: John Hinde,

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