3.5.3.7.7 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)