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 Computing14 151–160
Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
1: – doubleInput
On entry: , the first argument for which the bivariate Normal distribution function is to be evaluated.
2: – doubleInput
On entry: , the second argument for which the bivariate Normal distribution function is to be evaluated.
3: – doubleInput
On entry: , the correlation coefficient.
4: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
On any of the error conditions listed below g01hac returns .
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, .
On entry, .
Accuracy of the hybrid algorithm implemented here is discussed in Genz (2004). This algorithm should give a maximum absolute error of less than .
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g01hac makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The probabilities for the univariate Normal distribution can be computed using s15abcands15acc.
This example reads values of and for a bivariate Normal distribution along with the value of and computes the lower tail probabilities.