public static double s15ab(
	double x
)

Public Shared Function s15ab ( _
	x As Double _
) As Double

public:
static double s15ab(
	double x
)

static member s15ab : 
        x : float -> float 

s15ab returns the value of the cumulative Normal distribution function, $P\left(x\right)$.

s15ab evaluates an approximate value for the cumulative Normal distribution function The method is based on the fact that and it calls s15ad to obtain a value of $\mathit{erfc}$ for the appropriate argument.

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

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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, they are in principle related by so that the relative error in the argument, $x$, is amplified by a factor, $\frac{x{e}^{-\frac{1}{2}{x}^2}}{\sqrt{2\pi }P\left(x\right)}$, 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 $\sim x^2$ and hence to a certain extent relative accuracy is unavoidably lost.

However the absolute error in the result, $E$, is given by so absolute accuracy can be guaranteed for all $x$.

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