Kinhomhat function

Estimation of the inhomogenous K function

Estimates the Kinhom function

Kinhomhat(X, r = NULL, ReferenceType = "", lambda = NULL, CheckArguments = TRUE)

Arguments

• X: A weighted, marked, planar point pattern (wmppp.object).
• r: A vector of distances. If NULL, a sensible default value is chosen (512 intervals, from 0 to half the diameter of the window) following spatstat .
• 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.
• CheckArguments: Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.

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.

Returns

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

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.

Note

The computation of Kinhomhat relies on spatstat functions Kinhom, density.ppp and bw.diggle.

See Also

KinhomEnvelope, Kinhom

Examples

data(paracou16)

# Density of all trees
lambda <- density.ppp(paracou16, bw.diggle(paracou16))
plot(lambda)
# Reduce the point pattern to one type of trees
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
autoplot(Kinhomhat(paracou16, r, "V. Americana", lambda), ./(pi*r^2) ~ r)