nag_cumul_normal (s15abc) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_cumul_normal (s15abc)


    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
The function is based on the fact that
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


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


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)

nag_cumul_normal (s15abc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016