nag_bivariate_normal_dist (g01hac) returns the lower tail probability for the bivariate Normal distribution.
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).
Genz A (2004) Numerical computation of rectangular bivariate and trivariate Normal and probabilities Statistics and Computing 14 151–160
Accuracy of the hybrid algorithm implemented here is discussed in
Genz (2004). This algorithm should give a maximum absolute error of less than
.
Not applicable.
The probabilities for the univariate Normal distribution can be computed using
nag_cumul_normal (s15abc) and
nag_cumul_normal_complem (s15acc).