# khat

0th

Percentile

##### K-function

Calculates an estimate of the K-function

Keywords
spatial
##### Usage
khat(pts,poly,s,newstyle=FALSE)
print.khat(x, ...)
plot.khat(x, ...)
##### Arguments
pts
A points data set
poly
A polygon containing the points
s
A vector of distances at which to calculate the K function
newstyle
if TRUE, the function returns a khat object
x
a khat object
...
other arguments passed to plot and print functions
##### Details

The K function is defined as the expected number of further points within a distance s of an arbitrary point, divided by the overall density of the points. In practice an edge-correction is required to avoid biasing the estimation due to non-recording of points outside the polygon.

The newstyle argument and khat object were introduced in collaboration with Thomas de Cornulier to permit the mapping of counts or khats for chosen distance values, as in ftp://pbil.univ-lyon1.fr/pub/mac/ADE/ADE4/DocThemPDFUS/Thema81.pdf, p.18.

##### Value

• If newstyle is FALSE, a vector like s containing the value of K at the points in s. else a khat object list with:
• khatthe value of K at the points in s
• countsinteger matrix of counts of points within the vector of distances s for each point
• khatsmatrix of values of K within the vector of distances s for each point
• ss

##### References

Ripley, B.D. 1976 The second-order analysis of stationary point processes, J. Appl. Prob, 13 255-266; Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: http://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.

Kenv.csr

• khat
• print.khat
• plot.khat
##### Examples
data(cardiff)
s <- seq(2,30,2)
plot(s, sqrt(khat(as.points(cardiff), cardiff$poly, s)/pi) - s, type="l", xlab="Splancs - polygon boundary", ylab="Estimated L", ylim=c(-1,1.5)) newstyle <- khat(as.points(cardiff), cardiff$poly, s, newstyle=TRUE)
str(newstyle)
newstyle
apply(newstyle\$khats, 2, sum)
plot(newstyle)