# 3.5.3.2.8 Ksdensity

## Definition:

y=ksdensity(x, vX, w) returns the kernel density at x for a given vector vX with a bandwidth w, where an optimal w can be determined by the estimation function kernelwidth.

$\text{ksdensity}(x, \text{vX}, w)=\frac{1}{n}\sum_{i=1}^n \frac{1}{\sqrt{2\pi}w}e^{\frac{-(x-\text{vX}_i)^2}{2w^2}}$

where n is the size of vector vX, $\text{vX}_i$ is the ith element in vector vX.

## Parameters:

$x$ (input, double)
The value to be evaluated for density
$\text{vX}$ (input, vector)
Distributed samples used as kernel centers
$w$ (input, double)
Bandwidth used as kernel scale, $w > 0$
$y$ (output, double)
Kernel density