s15ab returns the value of the cumulative Normal distribution function, Px.

Syntax

C#
public static double s15ab(
	double x
)
Visual Basic
Public Shared Function s15ab ( _
	x As Double _
) As Double
Visual C++
public:
static double s15ab(
	double x
)
F#
static member s15ab : 
        x : float -> float 

Parameters

x
Type: System..::..Double
On entry: the argument x of the function.

Return Value

s15ab returns the value of the cumulative Normal distribution function, Px.

Description

s15ab evaluates an approximate value for the cumulative Normal distribution function
Px=12π-xe-u2/2du.
The method is based on the fact that
Px=12erfc-x2
and it calls s15ad to obtain a value of erfc for the appropriate argument.

References

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

Error Indicators and Warnings

ifail=-9000
An error occured, see message report.

Accuracy

Because of its close relationship with erfc, the accuracy of this method is very similar to that in s15ad. If ε and δ are the relative errors in result and argument, respectively, they are in principle related by
εxe-12x22πPxδ
so that the relative error in the argument, x, is amplified by a factor, xe-12x22πPx, 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
Exe-12x22πδ
so absolute accuracy can be guaranteed for all x.

Parallelism and Performance

None.

Further Comments

None.

Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

Example program (C#): s15abe.cs

Example program data: s15abe.d

Example program results: s15abe.r

See Also