kinhat
Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.
Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.
- Keywords
- spatial
Usage
kinhat(pts, lambda, poly, s)Arguments
- pts
matrix of the
x,y-coordinates of the point locations.- lambda
intensity function evaluated at the above point locations.
- poly
matrix of the
x,y-coordinates of the polygon boundary.- s
vector of distances at which to calculate the K function.
Details
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.
Value
A list with components
- k
values of estimated K at the distances
s.- s
copy of
s.
Note
This code is adapted from splancs (Rowlingson and Diggle, 1993)
fortran code for the estimation of homogeneous K function
khat, with edge correction inherited
for a general polygonal area.
References
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.