Computing Probability Integrals of a Bivariate Normal Distribution
by Saeed Maghsoodloo and Chien-Lung Huang.
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.
Bivariate Normal Integral, Matrix Transformation, Computer Software
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