NAG Library Function Document

nag_cumul_normal_complem (s15acc)

nag_cumul_normal_complem (s15acc) returns the value of the complement of the cumulative normal distribution function $Q\left(x\right)$.

nag_cumul_normal_complem (s15acc) evaluates an approximate value for the complement of 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, then in principle they are related by $\left|\epsilon \right|\simeq \left|\left({xe}^{-x^2/2}/\sqrt{2\pi }Q\left(x\right)\right)\delta \right|$.

For $x$ negative or small positive the multiplying 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 $\left|E\right|\simeq \left|\left({xe}^{-x^2/2}/\sqrt{2\pi }\right)\delta \right|$, 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.