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.

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

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.

- X
A window (object of class

`"owin"`

) or point pattern (object of class`"ppp"`

) or other data which can be converted to a window using`as.owin`

.- ...
Arguments passed to

`distcdf`

.- f
Probability value (between 0 and 1) determining the quantile of the distribution.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

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 \(F(r) \ge f\).

For estimating point process intensity, see
`density.ppp`

,
`bw.diggle`

,
`bw.ppl`

,
`bw.scott`

,
`bw.CvL`

.

For other smoothing purposes, see
`bw.stoyan`

,
`bw.smoothppp`

,
`bw.relrisk`

.

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

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