﻿ s15ac Method
s15ac returns the value of the complement of the cumulative Normal distribution function, $Q\left(x\right)$.

# Syntax

C#
```public static double s15ac(
double x
)```
Visual Basic
```Public Shared Function s15ac ( _
x As Double _
) As Double```
Visual C++
```public:
static double s15ac(
double x
)```
F#
```static member s15ac :
x : float -> float
```

#### Parameters

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

#### Return Value

s15ac returns the value of the complement of the cumulative Normal distribution function, $Q\left(x\right)$.

# Description

s15ac evaluates an approximate value for the complement of the cumulative Normal distribution function
 $Qx=12π∫x∞e-u2/2du.$
The method is based on the fact that
 $Qx=12erfcx2$
and it calls s15ad to obtain the necessary value of $\mathit{erfc}$, the complementary error function.

# References

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

None.

# Accuracy

Because of its close relationship with $\mathit{erfc}$ the accuracy of this method is very similar to that in s15ad. If $\epsilon$ and $\delta$ are the relative errors in result and argument, respectively, then in principle they are related by
 $ε≃xe-x2/22πQxδ.$
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 $\epsilon \sim {x}^{2}\delta$ and hence to a certain extent relative accuracy is unavoidably lost. However the absolute error in the result, $E$, is given by
 $E≃xe-x2/22πδ$
and since this factor is always less than one absolute accuracy can be guaranteed for all $x$.

None.

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#): s15ace.cs

Example program data: s15ace.d

Example program results: s15ace.r