NAG Library Routine Document
S15ABF returns the value of the cumulative Normal distribution function, , via the function name.
|REAL (KIND=nag_wp) S15ABF
S15ABF evaluates an approximate value for the cumulative Normal distribution function
The routine is based on the fact that
and it calls S15ADF
to obtain a value of
for the appropriate argument.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: X – REAL (KIND=nag_wp)Input
On entry: the argument of the function.
- 2: 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
There are no failure exits from this routine. The parameter IFAIL
is included for consistency with other routines in this chapter.
Because of its close relationship with
, the accuracy of this routine is very similar to that in S15ADF
are the relative errors in result and argument, respectively, they are in principle related by
so that the relative error in the argument,
, is amplified by a factor,
, in the result.
For small and for positive this factor is always less than one and accuracy is mainly limited by machine precision.
For large negative the factor behaves like and hence to a certain extent relative accuracy is unavoidably lost.
However the absolute error in the result,
, is given by
so absolute accuracy can be guaranteed for all
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s15abfe.f90)
9.2 Program Data
Program Data (s15abfe.d)
9.3 Program Results
Program Results (s15abfe.r)