# Ksector

0th

Percentile

##### Sector K-function

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.

Keywords
spatial, nonparametric
##### Usage
Ksector(X, begin = 0, end = 360, ...,
r = NULL, breaks = NULL,
correction = c("border", "isotropic", "Ripley", "translate"),
domain=NULL, ratio = FALSE, verbose=TRUE)
##### Arguments
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",
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.
##### Details

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.

##### Value

• An object of class "fv" containing the estimated function.

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