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

None.

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