Using Weight Functions in Spatial Point Pattern Analysis with Application to Plant Ecology Data

Abstract

A very common way of analyzing different and complicated plant behaviors is to use spatial point pattern analysis, which allows us to assess whether there is any structure present. To test the complete spatial randomness hypothesis, Diggle (1979) proposed a Monte Carlo test whose test statistic is the discrepancy between the estimated and the theoretical form of some summary function, such as the Ripley K-function. In this article, we improve this test by adding various weight functions and get more powerful tests if decreasing and increasing weight functions are used for processes with short and long, respectively, range of interaction.

Keywords:

• Complete spatial randomness
• Edge-correction
• K-function
• Monte Carlo simulation

Mathematics Subject Classification:

• 62M30
• 62P10

Acknowledgments

This research was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. HKBU2048/02P and HKBU200503) and an FRG grant of the Hong Kong Baptist University. We thank the referee for helpful comments.