A test for multidimensional clustering tendency (Q761799)

A multidimensional extension of the Cox-Lewis statistic for testing clustering tendency among random, aggregated and regular arrangements of points is considered. The distribution of the statistic is examined under the randomness hypothesis of a Poisson spatial point process. The probability densities of the Cox-Lewis statistic are given under lattice- regularity and under extreme clustering. The former is defined by the ''patterns filling a lattice of side a'', while the latter is a modification of the Thomas process. Invoking the central limit theorem, it is possible to develop the Neyman-Pearson tests based on Cox-Lewis statistic. The power of such procedures is given. In addition, the power structure of the Cox-Lewis statistic is studied for hard-core regularity and Neyman-Scott regularity. However, these studies are restricted to Monte Carlo simulations. The conclusion is that the statistic suggested, based on Cox-Lewis statistic, is of great promise.