edge.Ripley
Ripley's Isotropic Edge Correction
Computes Ripley's isotropic edge correction weights for a point pattern.
- Keywords
- spatial, nonparametric
Usage
edge.Ripley(X, r, W = X$window, method = "C", maxweight = 100)Arguments
- X
- Point pattern (object of class
"ppp"). - W
- Window for which the edge correction is required.
- r
- Vector or matrix of interpoint distances for which the edge correction should be computed.
- method
- Choice of algorithm. Either
"interpreted"or"C". This is needed only for debugging purposes. - maxweight
- Maximum permitted value of the edge correction weight.
Details
This function computes Ripley's (1977) isotropic edge correction weight, which is used in estimating the $K$ function and in many other contexts.
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.
Value
- A numeric vector or matrix.
References
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 -- 212.
See Also
Examples
v <- edge.Ripley(cells, pairdist(cells))