# edge.Ripley

##### Ripley's Isotropic Edge Correction

Computes Ripley's isotropic edge correction weights for a point pattern.

- Keywords
- spatial, nonparametric

##### Usage

`edge.Ripley(X, r, W = X$window, method = "C", maxweight = 100)`rmax.Ripley(W)

##### Arguments

- X
- Point pattern (object of class
`"ppp"`

). - W
- Window for which the edge correction is required.
- r
- Vector or matrix of interpoint distances for which the edge correction should be computed.
- method
- Choice of algorithm. Either
`"interpreted"`

or`"C"`

. This is needed only for debugging purposes. - maxweight
- Maximum permitted value of the edge correction weight.

##### Details

The function `edge.Ripley`

computes Ripley's (1977) isotropic edge correction
weight, which is used in estimating the $K$ function and in many
other contexts.

The function `rmax.Ripley`

computes the maximum value of
distance $r$ for which the isotropic edge correction
estimate of $K(r)$ is valid.
For a single point $x$ in a window $W$,
and a distance $r > 0$, the isotropic edge correction weight
is
$$e(u, r) = \frac{2\pi r}{\mbox{length}(c(u,r) \cap W)}$$
where $c(u,r)$ is the circle of radius $r$ centred at the
point $u$. The denominator is the length of the overlap between
this circle and the window $W$.

The function `edge.Ripley`

computes this edge correction weight
for each point in the point pattern `X`

and for each
corresponding distance value in the vector or matrix `r`

.
If `r`

is a vector, with one entry for each point in
`X`

, then the result is a vector containing the
edge correction weights `e(X[i], r[i])`

for each `i`

.

If `r`

is a matrix, with one row for each point in `X`

,
then the result is a matrix whose `i,j`

entry gives the
edge correction weight `e(X[i], r[i,j])`

.
For example `edge.Ripley(X, pairdist(X))`

computes all the
edge corrections required for the $K$-function.

If any value of the edge correction weight exceeds `maxwt`

,
it is set to `maxwt`

.

The function `rmax.Ripley`

computes the smallest distance $r$
such that it is possible to draw a circle of radius $r$, centred
at a point of `W`

, such that the circle does not intersect the
interior of `W`

.

##### Value

- A numeric vector or matrix.

##### References

Ripley, B.D. (1977)
Modelling spatial patterns (with discussion).
*Journal of the Royal Statistical Society, Series B*,
**39**, 172 -- 212.

##### See Also

##### Examples

```
v <- edge.Ripley(cells, pairdist(cells))
rmax.Ripley(Window(cells))
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*