R: Covariance matrix for the difference between two K-functions

khvc {splancs}

R Documentation

Covariance matrix for the difference between two K-functions

Description

Calculate the covariance matrix for the difference between two K-functions. Also return the contribution to the variance for each of the two point patterns,

Usage

khvc(pts1, pts2, poly, s)

Arguments

`pts1`	An object containing the case locations.
`pts2`	An object containing the control locations.
`poly`	A polygon enclosing the locations in `pts1` and `pts2`
`s`	A vector of distances at which the calculation is to be made.

Value

A list with four components:

`varmat`	The upper triangle of the covariance matrix.
`k11`	The variance of Khat for the cases
`k22`	The variance of Khat for the controls
`k12`	The covariance of Khat for the cases and Khat for controls.

Note

Note that the diagonal of the covariance matrix is $k11 - 2 * $k12 + $k22

References

Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.