Kernel2width

Definition:

kernel2width( vX, vY, wx, wy[, int method=0, int grid=32]) returns the 2D kernel density optimal bandwidths (wx, wy) of X scale and Y scale for datasets (vX, vY) using two different methods.

When method = 0 (default)

Bivariate Kernel Density Estimator method is used.

This method offers bandwidth based on linear diffusion process.

When method = 1

Rule of Thumb method is used.

The estimation of wx and wy simply can be calculated by:

\[w_x = \frac{\sigma_x}{2n^{1/6}}\]

\[w_y = \frac{\sigma_y}{2n^{1/6}}\]

where n is the size of vector vX or vY, \(\sigma_x\) is the sample standard variation for dataset vX, and \(\sigma_y\) for dataset vY accordingly.

Parameters:

vX (input, vector)

x values of distributed samples used to estimate bandwidth

vY (input, vector)

y values of distributed samples used to estimate bandwidth

wx (output, double)

output width for X scale, \(w_x > 0 \)

wy (output, double)

output width for Y scale, \(w_y > 0 \)

method (input, int)

method = 0 (default) for Bivariate Kernel Density Estimator method or 1 for Rule of Thumb method.

grid (input, int)

input number of grids in X/Y direction for method=0, grid is a positive integer.