in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

There is currently a gap in theory for point patterns that lie on the surface of objects, with researchers focusing Euclidean space, typically planar and spatial data. Methodology data thus relies geometry therefore inappropriate analysis observed non-Euclidean spaces. Recently, there has been extensions to sphere, however, many other shapes are left unexplored. This part due challenge defining...

To test for “randomness” in spatial point patterns, we propose two test statistics that are obtained by “reducing” two-dimensional point patterns to the one-dimensional one. Also the exact and asymptotic distribution of these statistics are drawn.

Ecological spatial patterns are structured by a multiplicity of processes acting over a wide range of scales. We propose a new method, based on the scalewise variance--that is, the variance as a function of spatial scale, calculated here with wavelet kernel functions--to disentangle the signature of processes that act at different and similar scales on observed spatial patterns. We derive exact...

to test for “randomness” in spatial point patterns, we propose two test statistics that are obtained by “reducing” two-dimensional point patterns to the one-dimensional one. also the exact and asymptotic distribution of these statistics are drawn.