A directional counterpart of Ripley's \(K\) function, in which pairs of points are counted only when the vector joining the pair happens to lie in a particular range of angles.

```
Ksector(X, begin = 0, end = 360, ...,
units = c("degrees", "radians"),
r = NULL, breaks = NULL,
correction = c("border", "isotropic", "Ripley", "translate"),
domain=NULL, ratio = FALSE, verbose=TRUE)
```

An object of class `"fv"`

containing the estimated
function.

- X
The observed point pattern, from which an estimate of \(K(r)\) will be computed. An object of class

`"ppp"`

, or data in any format acceptable to`as.ppp()`

.- begin,end
Numeric values giving the range of angles inside which points will be counted. Angles are measured in degrees (if

`units="degrees"`

, the default) or radians (if`units="radians"`

) anti-clockwise from the positive \(x\)-axis.- ...
Ignored.

- units
Units in which the angles

`begin`

and`end`

are expressed.- r
Optional. Vector of values for the argument \(r\) at which \(K(r)\) should be evaluated. Users are advised

*not*to specify this argument; there is a sensible default.- breaks
This argument is for internal use only.

- correction
Optional. A character vector containing any selection of the options

`"none"`

,`"border"`

,`"bord.modif"`

,`"isotropic"`

,`"Ripley"`

,`"translate"`

,`"translation"`

,`"none"`

,`"good"`

or`"best"`

. It specifies the edge correction(s) to be applied. Alternatively`correction="all"`

selects all options.- domain
Optional window. The first point \(x_i\) of each pair of points will be constrained to lie in

`domain`

.- ratio
Logical. If

`TRUE`

, the numerator and denominator of each edge-corrected estimate will also be saved, for use in analysing replicated point patterns.- verbose
Logical value indicating whether to print progress reports and warnings.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

This is a directional counterpart of Ripley's \(K\) function
(see `Kest`

) in which, instead of counting all
pairs of points within a specified distance \(r\), we
count only the pairs \((x_i, x_j)\)
for which the vector \(x_j - x_i\)
falls in a particular range of angles.

This can be used to evaluate evidence for anisotropy
in the point pattern `X`

.

`Kest`

```
K <- Ksector(swedishpines, 0, 90)
plot(K)
```

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