spatstat (version 1.64-1)

# bw.frac: Bandwidth Selection Based on Window Geometry

## Description

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

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.

## 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.

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

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.
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