S15ACF returns the value of the complement of the cumulative Normal distribution function, $Q\left(x\right)$, via the function name.
S15ACF evaluates an approximate value for the complement of the cumulative Normal distribution function
The routine is based on the fact that
and it calls
S15ADF to obtain the necessary value of
$\mathit{erfc}$, the complementary error function.
There are no failure exits from this routine. The parameter
IFAIL is included for consistency with other routines in this chapter.
Because of its close relationship with
$\mathit{erfc}$ the accuracy of this routine is very similar to that in
S15ADF. If
$\epsilon $ and
$\delta $ are the relative errors in result and argument, respectively, then in principle they are related by
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
and since this factor is always less than one absolute accuracy can be guaranteed for all
$x$.
None.