nag_cumul_normal_complem (s15acc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_cumul_normal_complem (s15acc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_cumul_normal_complem (s15acc) returns the value of the complement of the cumulative normal distribution function Q x .

2  Specification

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

3  Description

nag_cumul_normal_complem (s15acc) evaluates an approximate value for the complement of the cumulative normal distribution function
Q x = 1 2π x e - u 2 / 2 du .
The function is based on the fact that
Q 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, then in principle they are related by ε xe - x 2 / 2 / 2π Q x δ .
For x  negative or small positive the multiplying factor is always less than one and accuracy is mainly limited by machine precision. For large positive x  we find ε x 2 δ  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 (s15acce.c)

9.2  Program Data

Program Data (s15acce.d)

9.3  Program Results

Program Results (s15acce.r)


nag_cumul_normal_complem (s15acc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

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