# 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. 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 - ...
- 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
- 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 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.

`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))
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*