A third order point process characteristic

K. Schladitz, Adrian Baddeley

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    27 Citations (Scopus)


    Second order characteristics, in particular Ripley's K-function, are widely used for the statistical analysis of point patterns. We examine a third order analogue, namely the mean number T(r) of r-close triples of points per unit area. Equivalently this is the expected number of r-close point pairs in an r-neighbourhood of the typical point. Various estimators for this function are proposed and compared, and we give an explicit formula for the isotropic edge correction. The theoretical value of T seems to be unobtainable for most point process models apart from the homogeneous Poisson process. However, simulation studies show that the function T discriminates well between different types of point processes. In particular it detects a clear difference between the Poisson process and the Baddeley-Silverman cell process whereas the K-functions for these processes coincide.
    Original languageEnglish
    Pages (from-to)657-671
    JournalScandinavian Journal of Statistics
    Issue number4
    Publication statusPublished - 2000


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