NAG Library Function Document

nag_cumul_normal (s15abc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_cumul_normal (s15abc) returns the value of the cumulative Normal distribution function, Px.

2
Specification

#include <nag.h>
#include <nags.h>
double  nag_cumul_normal (double x)

3
Description

nag_cumul_normal (s15abc) evaluates an approximate value for the cumulative Normal distribution function
Px=12π-xe-u2/2du.  
The function is based on the fact that
Px=12erfc-x2  
and it calls nag_erfc (s15adc) to obtain a value of erfc for the appropriate argument.

4
References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5
Arguments

1:     x doubleInput
On entry: the argument x of the function.

6
Error Indicators and Warnings

None.

7
Accuracy

Because of its close relationship with erfc, the accuracy of this function is very similar to that in nag_erfc (s15adc). If ε and δ are the relative errors in result and argument, respectively, they are in principle related by
ε x e -12 x2 2πPx δ  
so that the relative error in the argument, x, is amplified by a factor, xe-12x2 2πPx , in the result.
For x small and for x positive this factor is always less than one 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

nag_cumul_normal (s15abc) is not threaded in any implementation.

9
Further Comments

None.

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 (s15abce.c)

10.2
Program Data

Program Data (s15abce.d)

10.3
Program Results

Program Results (s15abce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017