NAG FL Interface
s15abf (cdf_​normal)

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1 Purpose

s15abf returns the value of the cumulative Normal distribution function, P(x), via the function name.

2 Specification

Fortran Interface
Function s15abf ( x, ifail)
Real (Kind=nag_wp) :: s15abf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  s15abf_ (const double *x, Integer *ifail)
The routine may be called by the names s15abf or nagf_specfun_cdf_normal.

3 Description

s15abf evaluates an approximate value for the cumulative Normal distribution function
P(x) = 12π -x e-u2/2 du .  
The routine is based on the fact that
P(x) = 12 erfc(-x2)  
and it calls s15adf to obtain a value of erfc for the appropriate argument.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument x of the function.
2: ifail Integer Input/Output
There are no failure exits from this routine. The argument ifail is included for consistency with other routines in this chapter.

6 Error Indicators and Warnings


7 Accuracy

Because of its close relationship with erfc, the accuracy of this routine is very similar to that in s15adf. If ε and δ are the relative errors in result and argument, respectively, they are in principle related by
|ε| | x e -12 x2 2πP(x) δ|  
so that the relative error in the argument, x, is amplified by a factor, x e -12 x2 2πP(x) , in the result.
For x small and for x positive this factor is always less than 1 and accuracy is mainly limited by machine precision.
For large negative x the factor behaves like x2 and hence to a certain extent relative accuracy is unavoidably lost.
However, the absolute error in the result, E, is given by
|E| | x e -12 x2 2π δ|  
so absolute accuracy can be guaranteed for all x.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s15abf is not threaded in any implementation.

9 Further Comments


10 Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1 Program Text

Program Text (s15abfe.f90)

10.2 Program Data

Program Data (s15abfe.d)

10.3 Program Results

Program Results (s15abfe.r)