# 3.5.2.15 Kernelwidth

## Definition:

w = kernelwidth( vX ) returns the estimated optimal kernel bandwidth for a given vector vX.

$w = 0.9 \sigma n^{-\frac{1}{5}}$

where n is the size of vector vX, and

$\sigma = \min( \hat{\sigma}, \ IQR/1.349 )$

, $\hat{\sigma}$ is the standard deviation of vX, and IQR is the interquartile range of vX.

## Parameters:

vX (input, vector)
Distributed samples used to estimate bandwidth
w (output, double)
Estimated optimal bandwidth for kernel density, $w > 0$