3.5.3.2.9 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.

$\text{ksdensity}(x, \text{vX}, \text{w})=\frac{1}{ n\text{w} } \sum_{i=1}^n K \left( \frac{x-\text{vX}_i}{ \text{w} } \right)$

where n is the size of vector vX, K is the kernel function, Origin uses normal (Gaussian) kernel function, $K(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}$ , and $\text{vX}_i$ is the ith element in vector vX.