NAG CL Interface
s15acc (compcdf_​normal)

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1 Purpose

s15acc returns the value of the complement of the cumulative Normal distribution function, Q(x).

2 Specification

#include <nag.h>
double  s15acc (double x)
The function may be called by the names: s15acc, nag_specfun_compcdf_normal or nag_cumul_normal_complem.

3 Description

s15acc evaluates an approximate value for the complement of the cumulative Normal distribution function
Q(x) = 12π x e-u2/2 du .  
The function is based on the fact that
Q(x) = 12 erfc(x2)  
and it calls s15adc to obtain the necessary value of erfc, the complementary error function.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x double Input
On entry: the argument x of the function.

6 Error Indicators and Warnings


7 Accuracy

Because of its close relationship with erfc the accuracy of this function is very similar to that in s15adc. 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

s15acc 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 (s15acce.c)

10.2 Program Data

Program Data (s15acce.d)

10.3 Program Results

Program Results (s15acce.r)