K-function — khat • splancs

Calculates an estimate of the K-function

khat(pts,poly,s,newstyle=FALSE,checkpoly=TRUE)
# S3 method for khat
print(x, ...)
# S3 method for khat
plot(x, ...)

Arguments

pts: A points data set
poly: A polygon containing the points - must be a perimeter ring of points
s: A vector of distances at which to calculate the K function
newstyle: if TRUE, the function returns a khat object
checkpoly: if TRUE compare polygon area and polygon bounding box and convex hull areas to see whether the polygon object is malformed; may be set to FALSE if the polygon is known to be a ring of points
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 http://pbil.univ-lyon1.fr/R/pdf/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: https://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.

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)
#> List of 4
#>  $ khat  : num [1:15] 30.3 88.6 168 274.4 401.5 ...
#>  $ counts: int [1:168, 1:15] 0 0 1 2 1 0 0 1 2 0 ...
#>  $ khats : num [1:168, 1:15] 0 0 0.22 0.441 0.22 ...
#>  $ s     : num [1:15] 2 4 6 8 10 12 14 16 18 20 ...
#>  - attr(*, "class")= chr "khat"
newstyle
#>  [1]   30.31848   88.62523  167.95850  274.37766  401.46106  543.63622
#>  [7]  715.22877  909.69473 1123.65207 1375.54225 1661.75200 1929.58087
#> [13] 2250.68876 2565.17067 2871.96159
apply(newstyle$khats, 2, sum)
#>  [1]   30.31848   88.62523  167.95850  274.37766  401.46106  543.63622
#>  [7]  715.22877  909.69473 1123.65207 1375.54225 1661.75200 1929.58087
#> [13] 2250.68876 2565.17067 2871.96159
plot(newstyle)