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 = 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. 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 edge correction for each possible pair of pointsX[i], Y[j]
for alli
andj
.- …
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, gW
Optional. Set covariance of
W
, if it has already been computed. Not required ifW
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 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.
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
Examples
# NOT RUN {
v <- edge.Trans(cells)
rmax.Trans(Window(cells))
# }