naginterfaces.library.specfun.compcdf_​normal_​vector

naginterfaces.library.specfun.compcdf_normal_vector(x)

compcdf_normal_vector returns an array of values of the complement of the cumulative Normal distribution function, $Q\left(x\right)$.

For full information please refer to the NAG Library document for s15aq

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s15aqf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The argument $x_{\text{i}}$ of the function, for $\text{i}=1,2,\dots ,n$.

Returns

ffloat, ndarray, shape $\left(n\right)$

$Q\left(x_i\right)$, the function values.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Notes

compcdf_normal_vector evaluates approximate values for the complement of the cumulative Normal distribution function

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

for an array of arguments $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

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