R: Distribution Function of Interpoint Distance

distcdf {spatstat.core} | R Documentation

## Distribution Function of Interpoint Distance

### Description

Computes the cumulative distribution function of the distance between two independent random points in a given window or windows.

### Usage

      distcdf(W, V=W, ..., dW=1, dV=dW, nr=1024,
              regularise=TRUE, savedenom=FALSE)

### Arguments

`W` | A window (object of class `"owin"`) containing the first random point.
`V` | Optional. Another window containing the second random point. Defaults to `W`.
`...` | Arguments passed to `as.mask` to determine the pixel resolution for the calculation.
`dV, dW` | Optional. Probability densities (not necessarily normalised) for the first and second random points respectively. Data in any format acceptable to `as.im`, for example, a `function(x,y)` or a pixel image or a numeric value. The default corresponds to a uniform distribution over the window.
`nr` | Integer. The number of values of interpoint distance r for which the CDF will be computed. Should be a large value!
`regularise` | Logical value indicating whether to smooth the results for very small distances, to avoid discretisation artefacts.
`savedenom` | Logical value indicating whether to save the denominator of the double integral as an attribute of the result.

### Details

This command computes the Cumulative Distribution Function CDF(r) = Prob(T ≤ r) of the Euclidean distance T = |X1-X2| between two independent random points X1 and X2.

In the simplest case, the command `distcdf(W)`, the random points are assumed to be uniformly distributed in the same window `W`.

Alternatively the two random points may be uniformly distributed in two different windows `W` and `V`.

In the most general case the first point X1 is random in the window `W` with a probability density proportional to `dW`, and the second point X2 is random in a different window `V` with probability density proportional to `dV`. The values of `dW` and `dV` must be finite and nonnegative.

The calculation is performed by numerical integration of the set covariance function `setcov` for uniformly distributed points, and by computing the covariance function `imcov` in the general case. The accuracy of the result depends on the pixel resolution used to represent the windows: this is controlled by the arguments `...` which are passed to `as.mask`. For example use `eps=0.1` to specify pixels of size 0.1 units.

The arguments `W` or `V` may also be point patterns (objects of class `"ppp"`). The result is the cumulative distribution function of the distance from a randomly selected point in the point pattern, to a randomly selected point in the other point pattern or window.

If `regularise=TRUE` (the default), values of the cumulative distribution function for very short distances are smoothed to avoid discretisation artefacts. Smoothing is applied to all distances shorter than the width of 7 pixels.

### Value

An object of class `"fv"`, see `fv.object`, which can be plotted directly using `plot.fv`.

### Author(s)

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

### See Also

`setcov`, `as.mask`.

### Examples

     # The unit disc
     B <- disc()
     plot(distcdf(B))

[Package spatstat.core version 2.3-0 Index]