NAG Library Routine Document
G01HAF returns the lower tail probability for the bivariate Normal distribution, via the routine name.
|REAL (KIND=nag_wp) G01HAF
||X, Y, RHO
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
- 1: X – REAL (KIND=nag_wp)Input
On entry: , the first argument for which the bivariate Normal distribution function is to be evaluated.
- 2: Y – REAL (KIND=nag_wp)Input
On entry: , the second argument for which the bivariate Normal distribution function is to be evaluated.
- 3: RHO – REAL (KIND=nag_wp)Input
On entry: , the correlation coefficient.
- 4: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
If on exit then G01HAF 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
The probabilities for the univariate Normal distribution can be computed using S15ABF
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 (g01hafe.f90)
9.2 Program Data
Program Data (g01hafe.d)
9.3 Program Results
Program Results (g01hafe.r)