khat: K-function

In splancs: Spatial and Space-Time Point Pattern Analysis

K-function

Description

Calculates an estimate of the K-function

Usage

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

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.

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: 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.

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)

splancs documentation built on May 29, 2024, 6:22 a.m.