Spatial cluster detection using the number of connected components of a graph

Avner Bar-Hen (1) , Michel Koskas (2) , Nicolas Picard (3)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 MMIP - MMIP
3 Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement

The aim of this work is to detect spatial clusters. We link Erdös graph and Poisson point process. We give the probability distribution function (pdf) of the number of connected component for an Erdös graph and obtain the pdf of the number of cluster for a Poisson process. Using this result, we directly obtain a test for complete spatial randomness and also obtain the clusters that violates the CSR hypothesis. Border effects are computed. We illustrate our results on a tropical forest example.

Mots clés: Erdös graph; Point Process; cluster detection

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Avner Bar-Hen, Michel Koskas, Nicolas Picard. Spatial cluster detection using the number of connected components of a graph. 2007. ⟨hal-00197578⟩