splancs (version 2.01-4)

khat: K-function

Description

Calculates an estimate of the K-function

Usage

khat(pts,poly,s)

Arguments

pts

A points data set

poly

A polygon containing the points

s

A vector of distances at which to calculate the K function

Value

• A vector like s containing the value of K at the points in s.

METHOD

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.

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)
plot(seq(2,30,2), sqrt(khat(as.points(cardiff), cardiff$poly, 
seq(2,30,2))/pi)-seq(2,30,2), type="l", xlab="Splancs - polygon boundary", 
ylab="Estimated L", ylim=c(-1,1.5))