naginterfaces.library.specfun.cdf_​normal

naginterfaces.library.specfun.cdf_normal(x)

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

For full information please refer to the NAG Library document for s15ab

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s15abf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

pfloat

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

Notes

cdf_normal evaluates an approximate value for the cumulative Normal distribution function

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

The function is based on the fact that

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

and it calls erfc_real() to obtain a value of $\text{erfc}$ for the appropriate argument.

References

NIST Digital Library of Mathematical Functions