edge.Trans
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 = X$window,
exact = FALSE, paired = FALSE,
...,
trim = spatstat.options("maxedgewt"),
dx=NULL, dy=NULL,
give.rmax=FALSE)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. IfFALSE
, a fast algorithm will be used to compute the approximate value. - paired
- Logical value indicating whether
X
andY
are paired. IfTRUE
, compute the edge correction for corresponding pointsX[i], Y[i]
for alli
. IfFALSE
, compute the ed - ...
- 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
andY
. See Details. - give.rmax
- Logical. If
TRUE
, also compute the value ofrmax.Trans(W)
and return it as an attribute of the result. - g
- Optional. Set covariance of
W
.
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 usingoverlap.owin
, which can be quite slow. - if
exact=FALSE
(the default), the weights are computed rapidly by evaluating the set covariance functionsetcov
using the Fast Fourier Transform.
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
Examples
v <- edge.Trans(cells)
rmax.Trans(Window(cells))