Computes Ripley's isotropic edge correction weights for a point pattern.
edge.Ripley(X, r, W = Window(X), method = "C", maxweight = 100)rmax.Ripley(W)
Point pattern (object of class "ppp").
Window for which the edge correction is required.
Vector or matrix of interpoint distances for which the edge correction should be computed.
Choice of algorithm. Either "interpreted" or "C".
This is needed only for debugging purposes.
Maximum permitted value of the edge correction weight.
A numeric vector or matrix.
The function edge.Ripley
computes Ripley's (1977) isotropic edge correction
weight, which is used in estimating the \(K\) function and in many
other contexts.
The function rmax.Ripley computes the maximum value of
distance \(r\) for which the isotropic edge correction
estimate of \(K(r)\) is valid.
For a single point \(x\) in a window \(W\), and a distance \(r > 0\), the isotropic edge correction weight is $$ e(u, r) = \frac{2\pi r}{\mbox{length}(c(u,r) \cap W)} $$ where \(c(u,r)\) is the circle of radius \(r\) centred at the point \(u\). The denominator is the length of the overlap between this circle and the window \(W\).
The function edge.Ripley computes this edge correction weight
for each point in the point pattern X and for each
corresponding distance value in the vector or matrix r.
If r is a vector, with one entry for each point in
X, then the result is a vector containing the
edge correction weights e(X[i], r[i]) for each i.
If r is a matrix, with one row for each point in X,
then the result is a matrix whose i,j entry gives the
edge correction weight e(X[i], r[i,j]).
For example edge.Ripley(X, pairdist(X)) computes all the
edge corrections required for the \(K\)-function.
If any value of the edge correction weight exceeds maxwt,
it is set to maxwt.
The function rmax.Ripley computes the smallest distance \(r\)
such that it is possible to draw a circle of radius \(r\), centred
at a point of W, such that the circle does not intersect the
interior of W.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 -- 212.
# NOT RUN {
v <- edge.Ripley(cells, pairdist(cells))
rmax.Ripley(Window(cells))
# }
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