A Comparative Study on the Power of van Lieshout and Baddeley's J‐Function

Summary functions such as the empty space function F and the nearest neighbour distance distribution function G are often used as test statistics for point patterns. Van Lieshout and Baddeley recently proposed an alternative statistic, the J ‐function, which is defined as J = (1 — G )/(1 — F ). Theoretical advantages of the J ‐function over the F ‐ and G ‐statistics are that it measures the type, strength and range of interaction, and that it can be evaluated explicitly for a larger class of models. In this simulation study we investigate empirically how the power of tests based on J compares to that of tests based on F and G .