NAG Library Function Document

nag_cumul_normal (s15abc)

nag_cumul_normal (s15abc) returns the value of the cumulative Normal distribution function $P\left(x\right)$.

nag_cumul_normal (s15abc) evaluates the cumulative Normal distribution function The function is based on the fact that

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

None.

If $\epsilon$ and $\delta$ are the relative errors in result and argument, respectively, they are in principle related by $\left|\epsilon \right|\simeq \left|\left({xe}^{-x^2/2}/\sqrt{2\pi }P\left(x\right)\right)\delta \right|$.

For $x$ small and for $x$ positive the multiplying factor is always less than one and accuracy is mainly limited by machine precision. For large negative $x$ we find $\epsilon \sim x^2$ and hence to a certain extent relative accuracy is unavoidably lost. However, the absolute error in the result, $E$, is given by $\left|E\right|\simeq \left|\left({xe}^{-x^2/2}/\sqrt{2\pi }\right)\right|>\delta$, and since this multiplying factor is always less than one, absolute accuracy can be guaranteed for all $x$.

None.

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