splancs (version 2.01-9)

khat: 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

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

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.

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)