Description Usage Arguments Details Value Note References See Also

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

1 |

`pts` |
matrix of the |

`lambda` |
intensity function evaluated at the above point locations. |

`poly` |
matrix of the |

`s` |
vector of distances at which to calculate the K function. |

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.

A list with components

- k
values of estimated K at the distances

`s`

.- s
copy of

`s`

.

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.

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.

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