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oCumBiNorm( ) - Model Definition

Function Definition

Calculates the cumulative bivariate normal distribution with upper integral limits a and b, and correlation coefficient ρ .


The value returned by oCumBiNorm(x) is the probability that the first variable is less than a and the second variable is less than b, when the correlation between the variables is ρ .


Model Definition

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Model Approximation

The oCumBiNorm( ) function uses a numerical approximation of the model definition which produces values of M(a,b;ρ) within four decimal places of the true value. Assuming a <= 0, b <= 0, and ρ<= 0. The approximation is:




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In circumstances where one, two or all three of the variables are positive the following identities are used:

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