- Type: System..::..DoubleOn entry: , the first argument for which the bivariate Normal distribution function is to be evaluated.
- Type: System..::..DoubleOn entry: , the second argument for which the bivariate Normal distribution function is to be evaluated.
- Type: System..::..DoubleOn entry: , the correlation coefficient.Constraint: .
For the two random variables following a bivariate Normal distribution with
the lower tail probability is defined by:
For a more detailed description of the bivariate Normal distribution and its properties see Abramowitz and Stegun (1972) and Kendall and Stuart (1969). The method used is described by Genz (2004).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Genz A (2004) Numerical computation of rectangular bivariate and trivariate Normal and probabilities Statistics and Computing 14 151–160
Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
Errors or warnings detected by the method:
On entry, , or .If on exit then g01ha returns zero.
Accuracy of the hybrid algorithm implemented here is discussed in Genz (2004). This algorithm should give a maximum absolute error of less than .
This example reads values of and for a bivariate Normal distribution along with the value of and computes the lower tail probabilities.