R: Mean of a Function of Interpoint Distance

pairMean {spatstat.core} | R Documentation

## Mean of a Function of Interpoint Distance

### Description

Computes the mean value, or the double integral, of a specified function of the distance between two independent random points in a given window or windows.

### Usage

    pairMean(fun, W, V = NULL, ..., normalise = TRUE)

### Arguments

`fun` | A function in the R language which takes one argument.
`W` | A window (object of class `"owin"`) containing the first random point.
`V` | Optional. Another window containing the second random point. Defaults to `W`.
`...` | Further optional arguments passed to `distcdf` to determine the pixel resolution for the calculation and the probability distributions of the random points.
`normalise` | Logical value specifying whether to calculate the mean value (`normalise=TRUE`, the default) or the double integral (`normalise=FALSE`).

### Details

This command computes the mean value of `fun(T)` where `T` is the Euclidean distance T = |X1-X2| between two independent random points X1 and X2.

In the simplest case, the command `pairMean(fun, 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`. Other options are described in `distcdf`.

The algorithm uses `distcdf` to compute the cumulative distribution function of `T`, and `stieltjes` to compute the mean value of `fun(T)`.

If `normalise=TRUE` (the default) the result is the mean value of `fun(T)`. If `normalise=FALSE` the result is the double integral.

### Value

A single numeric value.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### See Also

`distcdf`

### Examples

       pairMean(function(d) { d^2 }, disc())

[Package spatstat.core version 2.4-4 Index]