# bw.frac

0th

Percentile

##### 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.

Keywords
methods, smooth, spatial
##### Usage
bw.frac(X, ..., f=1/4)
##### Arguments
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.
##### 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

• bw.frac
##### Examples
h <- bw.frac(letterR)
h
plot(h, main="bw.frac(letterR)")
Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)

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