Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.
kinhat(pts, lambda, poly, s)matrix of the x,y-coordinates of the point locations.
intensity function evaluated at the above point locations.
matrix of the x,y-coordinates of the polygon boundary.
vector of distances at which to calculate the K function.
A list with components
values of estimated K at the distances s.
copy of s.
The inhomogeneous K function is a generalization of the usual K function defined for a second-order intensity-reweighted stationary point process, proposed by Baddeley et\ al (2000).
When the true intensity function is unknown, and is to be estimated
from the same data as been used to estimate the K function,
a modified kernel density estimation implemented in lambdahat
with argument gpts=NULL
can be used to calculate the estimated intensity at data points.
See Baddeley et al (2000) for details,
and Diggle, P.J., et al (2006) for a cautious note.
Baddeley, A. J. and M?ller, J. and Waagepetersen R. (2000) Non and semi-parametric estimation of interaction in inhomogeneous point patterns, Statistica Neerlandica, 54, 3, 329--350.
Diggle, P.J., V. G\(\acute{\mathrm{o}}\)mez-Rubio, P.E. Brown, A.G. Chetwynd and S. Gooding (2006) Second-order analysis of inhomogeneous spatial point processes using case-control data, submitted to Biometrics.
Rowlingson, B. and Diggle, P. (1993) Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627--655.