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 function in the R language which takes one argument.
A window (object of class "owin") containing the
first random point.
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.
Logical value specifying whether to calculate the mean
value (normalise=TRUE, the default) or the
double integral (normalise=FALSE).
A single numeric value.
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.
# NOT RUN {
pairMean(function(d) { d^2 }, disc())
# }
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