# kinhat: Inhomogeneous K-function Estimation Estimate the... In spatialkernel: Non-Parametric Estimation of Spatial Segregation in a Multivariate Point Process

## Description

Inhomogeneous K-function Estimation Estimate the inhomogeneous K function of a non-stationary point pattern.

## Usage

 1 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

1. 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.

2. 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.

3. Rowlingson, B. and Diggle, P. (1993) Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627–655.

khat, lambdahat