# 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.

##### See Also

*Documentation reproduced from package spatialkernel, version 0.4-23, License: CC BY-NC-SA 4.0*