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.
/math-89931747d19faa5196bbca3dca0908e7.png "\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, /math-5ec535ff7ac97cd30c96c7a2a051d9f9.png "K(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}")
,
and /math-d42590de7df507482af1323d9ced6ebd.png "\text{vX}_i")
is the ith element in vector vX.
Parameters:
/math-9dd4e461268c8034f5c8564e155c67a6.png "x")
(input, double)- The value to be evaluated for density
/math-dc072f8459258f6cfa11f1d4178e8ffc.png "\text{vX}")
(input, vector)- Distributed samples used as kernel centers
/math-9453f4344502c4439082d0902918c8ce.png "\text{w}")
(input, double)- Bandwidth used as kernel scale,
/math-c0a4fcddaf0d3bebb210d9caca5ee17d.png "\text{w} > 0")
/math-415290769594460e2e485922904f345d.png "y")
(output, double)- Kernel density
Reference
Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. Chapman & Hall, London.