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I am using R's package spatstat to study the locational pattern of conflict events in Africa (around 8.000 points) using point pattern analysis techniques.

I was able to obtain the plot of $g(r)$, the pair correlation function, using the contour of the African continent as my study region. The size of the enclosing rectangle is around 8.546km by 10.423km.

Spatstat does a nice job and gives me the plot of $g(r)$, but I noticed that the computation is not performed for $r > 625km$. Looking at this reply and in the function's source code, I understood that spatstat uses a rule of thumb stating that the biggest $r$ for which to compute Ripley's K-function and its variations should not excede 25% of the shortest side of the rectangle enclosing the study region.

My questions are thus the following:

  1. Is this rule of thumb also valid for complex polygons as it is for rectangles?
  2. What happens to my K-function if I compute it for a larger $r$ than what is advised?
  3. Is there any literature addressing this specific problem (size of $r$, polygonal windows)?
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  • $\begingroup$ Could you make the dataset available so it is possible to have a closer look at the problem? $\endgroup$
    – Ege Rubak
    Commented Dec 12, 2014 at 22:50
  • $\begingroup$ Regarding point 2: You simply get an estimate with a very large variance, so the true K-function for the underlying random phenomenon may be quite far from what you see in the estimate. $\endgroup$
    – Ege Rubak
    Commented Dec 12, 2014 at 22:53

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