naginterfaces.library.stat.pdf_​normal

naginterfaces.library.stat.pdf_normal(x, xmean, xstd)

pdf_normal returns the value of the probability density function (PDF) for the Normal (Gaussian) distribution with mean $\mu$ and variance ${\sigma }^2$ at a point $x$.

For full information please refer to the NAG Library document for g01ka

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/g01/g01kaf.html

Parameters

xfloat

$x$, the value at which the PDF is to be evaluated.

xmeanfloat

$\mu$, the mean of the Normal distribution.

xstdfloat

$\sigma$, the standard deviation of the Normal distribution.

Returns

pdffloat

The value of the PDF.

Raises

NagValueError

(errno $1$)

On entry, $xstd=⟨value⟩$.

Constraint: $xstd\times \sqrt{2.0\pi }>U$, where $U$ is the safe range parameter as defined by machine.real_safe.

(errno $2$)

Computation abandoned owing to underflow of $\frac{1}{(\sigma \times \sqrt{2\pi })}$.

(errno $3$)

Computation abandoned owing to an internal calculation overflowing.

Notes

The Normal distribution has probability density function (PDF)

$$f\left(x\right)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-{(x-\mu )}^2/2{\sigma }^2}\text{,}\sigma >0\text{.}$$