# bw.frac

##### Bandwidth Selection Based on Window Geometry

Select a smoothing bandwidth for smoothing a point pattern, based only on the geometry of the spatial window. The bandwidth is a specified quantile of the distance between two independent random points in the window.

##### Usage

`bw.frac(X, ..., f=1/4)`

##### Arguments

##### Details

This function selects an appropriate bandwidth `sigma`

for the kernel estimator of point process intensity
computed by `density.ppp`

.

The bandwidth $\sigma$ is computed as a quantile of the distance between two independent random points in the window. The default is the lower quartile of this distribution.

If $F(r)$ is the cumulative distribution function of the distance between two independent random points uniformly distributed in the window, then the value returned is the quantile with probability $f$. That is, the bandwidth is the value $r$ such that $F(r) = f$.

The cumulative distribution function $F(r)$ is
computed using `distcdf`

. We then
we compute the smallest number $r$
such that $F(r) \ge f$.

##### Value

- A numerical value giving the selected bandwidth.
The result also belongs to the class
`"bw.frac"`

which can be plotted to show the cumulative distribution function and the selected quantile.

##### See Also

`density.ppp`

,
`bw.diggle`

,
`bw.relrisk`

,
`bw.scott`

,
`bw.smoothppp`

,
`bw.stoyan`

##### Examples

```
h <- bw.frac(letterR)
h
plot(h, main="bw.frac(letterR)")
```

*Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)*