naginterfaces.library.stat.pdf_​normal_​vector

naginterfaces.library.stat.pdf_normal_vector(ilog, x, xmu, xstd)

pdf_normal_vector returns a number of values of the probability density function (PDF), or its logarithm, for the Normal (Gaussian) distributions.

For full information please refer to the NAG Library document for g01kq

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/g01/g01kqf.html

Parameters

ilogint

The value of $ilog$ determines whether the logarithmic value is returned in PDF.

$ilog=0$

$f(x_i,{\mu }_i,{\sigma }_i)$, the probability density function is returned.

$ilog=1$

$\log \left(f(x_i,{\mu }_i,{\sigma }_i)\right)$, the logarithm of the probability density function is returned.

xfloat, array-like, shape $\left(\text{lx}\right)$

$x_i$, the values at which the PDF is to be evaluated.

xmufloat, array-like, shape $\left(\text{lxmu}\right)$

${\mu }_i$, the means.

xstdfloat, array-like, shape $\left(\text{lxstd}\right)$

${\sigma }_i$, the standard deviations.

Returns

pdffloat, ndarray, shape $(max(\text{lx},\text{lxstd}))$

$f(x_i,{\mu }_i,{\sigma }_i)$ or $\log \left(f(x_i,{\mu }_i,{\sigma }_i)\right)$.

ivalidint, ndarray, shape $(max(\text{lx},\text{lxstd}))$

$ivalid[i-1]$ indicates any errors with the input arguments, with

$ivalid[i-1]=0$

No error.

$ivalid[i-1]=1$

${\sigma }_i<0$.

Raises

NagValueError

(errno $2$)

On entry, $ilog=⟨value⟩$.

Constraint: $ilog=0$ or $1$.

(errno $3$)

On entry, $\text{array size}=⟨value⟩$.

Constraint: $\text{lx}>0$.

(errno $4$)

On entry, $\text{array size}=⟨value⟩$.

Constraint: $\text{lxmu}>0$.

(errno $5$)

On entry, $\text{array size}=⟨value⟩$.

Constraint: $\text{lxstd}>0$.

Warns

NagAlgorithmicWarning

(errno $1$)

On entry, at least one value of $xstd$ was invalid.

Check $ivalid$ for more information.

Notes

The Normal distribution with mean ${\mu }_i$, variance ${\sigma }_i^2$; has probability density function (PDF)

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

The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See the G01 Introduction for further information.