Connectivity function and cumulative connectivity function.

Description

Amount of network connected pairs as a function of distance.

Usage

1
confun(x, r, R, h, adjust = 1, preGraph = NULL, ...)

Arguments

x

Point pattern

r

Vector of distances to estimate the function

R

The radius for generating the network, as geometric graph.

h

Smoothing parameter. h=0 and h>0 mean different things, see Details.

adjust

Adjust h by this factor (default=1).

preGraph

Precomputed network/graph, as a spatgraph-object. Alternative to R.

...

ignored.

Details

If h=0 we compute the cumulative version of the connecitivity function, corresponding to Ripley's K-function under the condition that the points in each pair must belong to the same component in an underlying network.

The underlying network can be given, or it will be computed as a geometric graph with parameter 'R'. If given as 'preGraph', it must be a spatgraphs-object, with same dimensions as the point pattern.

If h>0: Compute the probability of a pair being in the same component given their distance is ~ r. Uses kernel smoothing with bandwidth h.

Sensible defaults are computed for h and R if not given.

Border correction is done via translation correction. The bias is unknown as the network censoring is quite complex.

Theoretical values are unknown due to the graph conditioning.

Value

fv-object, see spatstat for more. Theoretical values unknown.

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
## Not run: 
x <- rMatClust(10, 0.1, 10)
plot(Cx<-confun(x,h=0, R=0.1))

# fit wrong model
ftho <- thomas.estpcf(x)
yf <- function()rThomas(ftho$par[1], ftho$par[2], x$n/ftho$par[1])
CC <- envelope(x, fun=confun, h=0, sim=yf, R=0.1)
C <- envelope(x, fun=confun, sim=yf, R=0.1)

plot(CC)
plot(C)

## End(Not run)