You can also have a look at:
DIGGLE P, ZHENG PP & DURR P (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. Journal of the Royal Statistical Society Series C-Applied Statistics 54, 645-658.
(The method is already implemented in R: spatialkernel)

With regards to the use of the bivariate K-function yu can find similar applications to yours in: FORTIN MJ & DALE MRT (2005) Spatial analysis: A guide for ecologists, 1st Edn. Cambridge University Press, Cambridge, UK.

berto costa rica wrote:
Dear list,

I want to assess if a series of cases (farms positive for a disease) are spatially clustered by comparing them to the general population (the total number of farms) in a given region. For that I would like to know if it is statistically correct to use the bivariate (also known as cross) k-function, considering cases as element 1 and general population (all farms, including the cases) as element 2. I am using splancs (k12hat function) in R. I know that you can do the difference of k-functions but I would like to know if the use of the bivariate k-function is correct. If it is statistically correct, can I conclude that the positive farms are clustered/dispersed compared to the total population (using label permutation)?

Thanks in advance for your help

albert

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