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

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 P x .

2  Specification

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

3  Description

nag_cumul_normal (s15abc) evaluates the cumulative Normal distribution function
P x = 1 2π - x e - u 2 / 2 du .
The function is based on the fact that
P x = 1 2 erfc -x / 2 .

4  References

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

5  Arguments

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

6  Error Indicators and Warnings

None.

7  Accuracy

If ε  and δ  are the relative errors in result and argument, respectively, they are in principle related by ε xe - x 2 / 2 / 2π P x δ .
For x  small and for x  positive the multiplying factor is always less than one and accuracy is mainly limited by machine precision. For large negative x  we find ε x 2  and hence to a certain extent relative accuracy is unavoidably lost. However, the absolute error in the result, E , is given by E xe - x 2 / 2 / 2π > δ , and since this multiplying factor is always less than one, absolute accuracy can be guaranteed for all x .

8  Further Comments

None.

9  Example

The following program reads values of the argument x  from a file, evaluates the function at each value of x  and prints the results.

9.1  Program Text

Program Text (s15abce.c)

9.2  Program Data

Program Data (s15abce.d)

9.3  Program Results

Program Results (s15abce.r)


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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012