# Kernel2width

Kernel2width-func

## 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:

where *n* is the size of vector vX or vY, is the sample standard variation for dataset vX, and 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,
- wy (output, double)
- output width for Y scale,
- 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.