khat {splancs}R Documentation

K-function

Description

Calculates an estimate of the K-function

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 <oedic@cebc.cnrs.fr> 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:

khat the value of K at the points in s
counts integer matrix of counts of points within the vector of distances s for each point
khats matrix of values of K within the vector of distances s for each point
s s

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.

See Also

Kenv.csr

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)

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