NAG Library Function Document
nag_bivariate_normal_dist (g01hac) returns the lower tail probability for the bivariate Normal distribution.
||nag_bivariate_normal_dist (double x,
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
x – doubleInput
On entry: , the first argument for which the bivariate Normal distribution function is to be evaluated.
y – doubleInput
On entry: , the second argument for which the bivariate Normal distribution function is to be evaluated.
rho – doubleInput
On entry: , the correlation coefficient.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
- On any of the error conditions listed below nag_bivariate_normal_dist (g01hac) returns .
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
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
The probabilities for the univariate Normal distribution can be computed using nag_cumul_normal (s15abc)
and nag_cumul_normal_complem (s15acc)
This example reads values of and for a bivariate Normal distribution along with the value of and computes the lower tail probabilities.
9.1 Program Text
Program Text (g01hace.c)
9.2 Program Data
Program Data (g01hace.d)
9.3 Program Results
Program Results (g01hace.r)