Used (Lived) versus Offered (Plain) densities of human settlement in space: An instance of the probabilistic consumption model

To people living in areas, the denser is the area, the more numerous are the opportunities of interpersonal and social interaction, of employment and of amenities of all kinds. The spatial density of human settlement is basically studied according to places, that is, area weighted. The notion of population-weighted density, or lived density, puts human density in the perspective of the people that experience it. Considering, respectively, the land units and the people as statistical populations of their own, the article provides a probabilistic model of human density in a geographical space, as a random variable in each statistical population, with specific probability density functions (PDFs) and cumulative distribution functions. The PDF of lived, “Used density” is derived from that of the plain, “Offered density” through a consumption model: Thus, their relationship is a specific instance of a well-established probabilistic model. The average used density is systematically larger than its offered counterpart: The ratio amounts to one plus the squared coefficient of variation of offered density. The relation between the two statistical distributions is illustrated using a Lorenz curve; the associated Gini index constitutes an indicator of population heterogeneity in a geographical space. A case of France’s population as of 2019 is studied to demonstrate the methodology.