NAG FL Interface
s15acf (compcdf_​normal)

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1 Purpose

s15acf returns the value of the complement of the cumulative Normal distribution function, Q(x), via the function name.

2 Specification

Fortran Interface
Function s15acf ( x, ifail)
Real (Kind=nag_wp) :: s15acf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  s15acf_ (const double *x, Integer *ifail)
The routine may be called by the names s15acf or nagf_specfun_compcdf_normal.

3 Description

s15acf evaluates an approximate value for the complement of the cumulative Normal distribution function
Q(x) = 12π x e-u2/2 du .  
The routine is based on the fact that
Q(x) = 12 erfc(x2)  
and it calls s15adf to obtain the necessary value of erfc, the complementary error function.

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, then in principle they are related by
|ε| | x e -x2/2 2πQ(x) δ| .  
For x negative or small positive this factor is always less than 1 and accuracy is mainly limited by machine precision. For large positive x we find εx2δ 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 -x2/2 2π δ|  
and since this factor is always less than one absolute accuracy can be guaranteed for all x.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
s15acf 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 (s15acfe.f90)

10.2 Program Data

Program Data (s15acfe.d)

10.3 Program Results

Program Results (s15acfe.r)