R: Ripley's Isotropic Edge Correction

edge.Ripley {spatstat.core} | R Documentation

## Ripley's Isotropic Edge Correction

### Description

Computes Ripley's isotropic edge correction weights for a point pattern.

### Usage

    edge.Ripley(X, r, W = Window(X), method = c("C", "interpreted"),
                maxweight = 100, internal=list())

    rmax.Ripley(W)

### 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.
`internal` | For developer use only.

### Details

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) = 2 * π * r/length(intersection(c(u,r), 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`.

### Value

A numeric vector or matrix.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 – 212.

### See Also

`edge.Trans`, `rmax.Trans`, `Kest`

### Examples

      v <- edge.Ripley(cells, pairdist(cells))

      rmax.Ripley(Window(cells))

[Package spatstat.core version 2.0-0 Index]