# edge.Trans

0th

Percentile

##### Translation Edge Correction

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

Keywords
spatial, nonparametric
edge.Trans(X, Y = X, W = X$window, exact = FALSE, paired = FALSE, trim = spatstat.options("maxedgewt")) ##### Arguments X,Y Point patterns (objects of class "ppp"). W Window for which the edge correction is required. exact Logical. If TRUE, a slow algorithm will be used to compute the exact value. If FALSE, a fast algorithm will be used to compute the approximate value. paired Logical value indicating whether X and Y are paired. If TRUE, compute the edge correction for corresponding points X[i], Y[i] for all i. If FALSE, compute the ed trim Maximum permitted value of the edge correction weight. ##### Details This function computes Ohser and Stoyan's translation edge correction weight, which is used in estimating the$K$function and in many other contexts. For a pair of points$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,

• ifexact=TRUE, the edge correction weights are computed exactly usingoverlap.owin, which can be quite slow.
• ifexact=FALSE(the default), the weights are computed rapidly by evaluating the set covariance functionsetcovusing the Fast Fourier Transform.
If any value of the edge correction weight exceeds trim, it is set to trim.

##### 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.

edge.Ripley, setcov, Kest
v <- edge.Trans(cells)