spatstat.explore (version 3.1-0)

edge.Ripley: 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)

Value

A numeric vector or matrix.

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.

Author

Adrian Baddeley

and Rolf Turner

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 $$ e(u, r) = \frac{2\pi r}{\mbox{length}(c(u,r) \cap W)} $$ 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.

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))