Given a point pattern X and another spatial object Y,
these functions compute two nonparametric measures of association
between X and Y, introduced by Foxall
(Foxall and Baddeley, 2002).
Let the random variable \(R\) be the distance from a typical point
of X to the object Y.
Foxall's \(G\)-function is the cumulative distribution function
of \(R\):
$$G(r) = P(R \le r)$$
Let the random variable \(S\) be the distance from a fixed point
in space to the object Y. The cumulative distribution function
of \(S\) is the (unconditional) spherical contact distribution
function
$$H(r) = P(S \le r)$$
which is computed by Hest.
Foxall's \(J\)-function is the ratio
$$
J(r) = \frac{1-G(r)}{1-H(r)}
$$
For further interpretation, see Foxall and Baddeley (2002).
Accuracy of Jfox depends on the pixel resolution,
which is controlled by the
arguments eps, dimyx and xy passed to
as.mask. For example, use eps=0.1 to specify
square pixels of side 0.1 units, and dimyx=256 to specify a
256 by 256 grid of pixels.