dbmss (version 1.2.4)

Kinhom.r: Estimation of the inhomogenous K function

Description

Estimates the Kinhom function

Usage

Kinhom.r(X, r, ReferenceType = "", lambda=NULL)

Arguments

X

A point pattern (ppp.object), marks must be a dataframe with two columns: PointType: labels, as factors. PointWeight: weights (ignored in computation).

r

A vector of distances.

ReferenceType

One of the point types. Default is all point types.

lambda

An estimation of the point pattern density, obtained by the density.ppp function.

Value

• A vector containing Kinhom(r) values.

Details

Kinhom is a cumulative, topographic measure of an inhomogenous point pattern structure. By default, density estimation is performed at points by density.ppp using the optimal bandwith (bw.diggle). It can be calculated separately (see example), including at pixels if the point pattern is too large for the default estimation to succeed, and provided as the argument lambda: Arbia et al. (2012) for example use another point pattern as a reference to estimate density. Bivariate Kinhom is not currently supported.

References

Baddeley, A. J., J. Moller, et al. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54(3): 329-350. Arbia, G., G. Espa, et al. (2012). Clusters of firms in an inhomogeneous space: The high-tech industries in Milan. Economic Modelling 29(1): 3-11.

See Also

KinhomEnvelope, Kinhom

Examples

data(paracou16)

# Density of all trees
lambda <- density.ppp(paracou16, bw.diggle(paracou16))
plot(lambda)
V.americana <- paracou16[paracou16$marks$PointType=="V. Americana"]
plot(V.americana, add=TRUE)

# Calculate Kinhom according to the density of all trees
r <- 0:30
ActualValues.X <- Kinhom.r(paracou16, r, "V. Americana", lambda)

# Plot
PlotResults(r, DivideByPiR2(ActualValues.X, r), ylab="Kinhom / (pi R^2)", ReferenceValue=1)