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.

Parameters:

\(x\) (input, double)

The value to be evaluated for density

\(\text{vX}\) (input, vector)

Distributed samples used as kernel centers

\(\text{w}\) (input, double)

Bandwidth used as kernel scale, \(\text{w} > 0\)

\(y\) (output, double)

Kernel density

Reference

Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. Chapman & Hall, London.