A comparative study on the power of van Lieshout and Baddeley's J-function

Abstract

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