Distance-based measures of spatial concentration: Introducing a relative density function

For a decade, distance-based methods have been widely employed and constantly improved in the field of spatial economics. These methods are a very useful tool for accurately evaluating the spatial distribution of plants or retail stores, for example (Duranton and Overman, 2008). In this paper, we introduce a new distance-based statistical measure for evaluating the spatial concentration of economic activities. To our knowledge, the m function is the first relative density function to be proposed in the economics literature. This tool supplements the typology of distance-based methods recently drawn up by Marcon and Puech (2012). By considering several theoretical and empirical examples, we show the advantages and the limits of the m function for detecting spatial structures in economics.