naginterfaces.library.specfun.compcdf_​normal

naginterfaces.library.specfun.compcdf_normal(x)

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

For full information please refer to the NAG Library document for s15ac

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s15acf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

qfloat

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

Notes

compcdf_normal evaluates an approximate value for the complement of the cumulative Normal distribution function

$$Q\left(x\right)=\frac{1}{\sqrt{2\pi }}{\int }_x^{\infty }{e}^{-u^2/2}du\text{.}$$

The function is based on the fact that

$$Q\left(x\right)=\frac{1}{2}erfc\left(\frac{x}{\sqrt{2}}\right)$$

and it calls erfc_real() to obtain the necessary value of $\text{erfc}$, the complementary error function.

References

NIST Digital Library of Mathematical Functions