nag_cumul_normal_complem (s15acc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG 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, Qx.

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
Qx=12πxe-u2/2du.
The function is based on the fact that
Qx=12erfcx2
and it calls nag_erfc (s15adc) to obtain the necessary value of erfc, the complementary error function.

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

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, then in principle they are related by
ε x e -x2/2 2πQx δ .
For x negative or small positive this factor is always less than one 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

Not applicable.

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 (s15acce.c)

10.2  Program Data

Program Data (s15acce.d)

10.3  Program Results

Program Results (s15acce.r)


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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014