Ks2density

Definition:

z = ks2density(x, y, vX, vY, wx, wy) returns the 2D kernel density at point (x, y) with respect
to a function established by datasets (vX, vY) with scale (wx, wy), where scale (wx, wy) are determined by estimation function Kernel2width.

\[\text{ks2density}(x,y,\text{vX},\text{vY},w_x,w_y) = \frac{1}{n} \sum_{i=1}^{n} \frac{1}{ 2\pi w_x w_y } \exp \left(-\frac{(x-\text{vX}_i)^2}{2w_x ^2} - \frac{(y-\text{vY}_i)^2}{2w_y^2} \right)\]

where n is the number of elements in vector vX or vY, \(\text{vX}_i\) is ith element in vector vX and \(\text{vY}_i\) is ith element in vector vY.

Parameters:

\(x\) (input, double)

x value to evaluate for 2D kernel density

\(y\) (input, double)

y value to evaluate for 2D kernel density

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

x values of distributed samples used as kernel centers

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

y values of distributed samples used as kernel centers

\(w_x\) (input, double)

The bandwidth of X scale, \(w_x > 0\)

\(w_y\) (input, double)

The bandwidth of Y scale, \(w_y > 0\)

\(z\) (output, double)

2D kernel density at point \((x,y)\) with respect to a function established by datasets (vX,vY) with scale \((w_x,w_y)\)