splancs (version 2.01-40)

# khat: K-function

## Description

Calculates an estimate of the K-function

## Usage

```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 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.

`Kenv.csr`

## Examples

```# NOT RUN {
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)
# }
```