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.

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

A single numeric value.

- 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`

).

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

This command computes the mean value of
`fun(T)`

where `T`

is
the Euclidean distance \(T = \|X_1 - X_2\|\)
between two independent random points \(X_1\) and \(X_2\).

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.

`distcdf`

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

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