edge.Ripley

0th

Percentile

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

edge.Trans, Kest

Aliases
  • edge.Ripley
Examples
v <- edge.Ripley(cells, pairdist(cells))
Documentation reproduced from package spatstat, version 1.37-0, License: GPL (>= 2)

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