edge.Trans

0th

Percentile

Translation Edge Correction

Computes Ohser and Stoyan's translation edge correction weights for a point pattern.

Keywords
spatial, nonparametric
Usage
edge.Trans(X, Y = X, W = Window(X),
      exact = FALSE, paired = FALSE,
      ..., 
      trim = spatstat.options("maxedgewt"),
      dx=NULL, dy=NULL,
      give.rmax=FALSE, gW=NULL)

rmax.Trans(W, g=setcov(W))

Arguments
X,Y

Point patterns (objects of class "ppp").

W

Window for which the edge correction is required.

exact

Logical. If TRUE, a slow algorithm will be used to compute the exact value. If FALSE, a fast algorithm will be used to compute the approximate value.

paired

Logical value indicating whether X and Y are paired. If TRUE, compute the edge correction for corresponding points X[i], Y[i] for all i. If FALSE, compute the edge correction for each possible pair of points X[i], Y[j] for all i and j.

Ignored.

trim

Maximum permitted value of the edge correction weight.

dx,dy

Alternative data giving the \(x\) and \(y\) coordinates of the vector differences between the points. Incompatible with X and Y. See Details.

give.rmax

Logical. If TRUE, also compute the value of rmax.Trans(W) and return it as an attribute of the result.

g, gW

Optional. Set covariance of W, if it has already been computed. Not required if W is a rectangle.

Details

The function edge.Trans computes Ohser and Stoyan's translation edge correction weight, which is used in estimating the \(K\) function and in many other contexts.

The function rmax.Trans computes the maximum value of distance \(r\) for which the translation edge correction estimate of \(K(r)\) is valid.

For a pair of points \(x\) and \(y\) in a window \(W\), the translation edge correction weight is $$ e(u, r) = \frac{\mbox{area}(W)}{\mbox{area}(W \cap (W + y - x))} $$ where \(W + y - x\) is the result of shifting the window \(W\) by the vector \(y - x\). The denominator is the area of the overlap between this shifted window and the original window.

The function edge.Trans computes this edge correction weight. If paired=TRUE, then X and Y should contain the same number of points. The result is a vector containing the edge correction weights e(X[i], Y[i]) for each i.

If paired=FALSE, then the result is a matrix whose i,j entry gives the edge correction weight e(X[i], Y[j]).

Computation is exact if the window is a rectangle. Otherwise,

  • if exact=TRUE, the edge correction weights are computed exactly using overlap.owin, which can be quite slow.

  • if exact=FALSE (the default), the weights are computed rapidly by evaluating the set covariance function setcov using the Fast Fourier Transform.

If any value of the edge correction weight exceeds trim, it is set to trim.

The arguments dx and dy can be provided as an alternative to X and Y. If paired=TRUE then dx,dy should be vectors of equal length such that the vector difference of the \(i\)th pair is c(dx[i], dy[i]). If paired=FALSE then dx,dy should be matrices of the same dimensions, such that the vector difference between X[i] and Y[j] is c(dx[i,j], dy[i,j]). The argument W is needed.

The value of rmax.Trans is the shortest distance from the origin \((0,0)\) to the boundary of the support of the set covariance function of W. It is computed by pixel approximation using setcov, unless W is a rectangle, when rmax.Trans(W) is the length of the shortest side of the rectangle.

Value

Numeric vector or matrix.

References

Ohser, J. (1983) On estimators for the reduced second moment measure of point processes. Mathematische Operationsforschung und Statistik, series Statistics, 14, 63 -- 71.

See Also

rmax.Trans, edge.Ripley, setcov, Kest

Aliases
  • edge.Trans
  • rmax.Trans
Examples
# NOT RUN {
  v <- edge.Trans(cells)
  rmax.Trans(Window(cells))
# }
Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)

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