Benford's law and geographical information - the example of OpenStreetMap

Few laws about geographical information are known, partly because geographical information is inherently complex. Tobler's first law of Geography and, to a lesser degree, also his second law are among the rare exceptions. In this article, we explore the validity of Benford's law in the context of the example of OpenStreetMap. More specifically, we compare the distribution of several numerical features of geographical entities to the Benford distribution. It is demonstrated that the numerical features examined are in accordance with Benford's law to a varying degree with little variation between the types of geographical entities. Spatial patterns in the deviation from Benford's law are shown to be similar for some aspects but to strongly differ for other ones. We show that many aspects of the data tend to deviate more than average from the Benford distribution in Africa, Greenland, smaller island countries, and, to a lesser degree, in South America. Also, the scale-dependency of Benford's law is explored. Motivated by the use of Benford's law to detect indications for fraud in economic and other datasets, future prospects and limitations to systematically develop intrinsic data quality measures are discussed.

Automated summary

There are few laws regarding geographical information due to its inherent complexity. This article explores the validity of Benford's law in the context of OpenStreetMap and finds that some geographical entities adhere to this law to varying degrees, with significant deviations in different regions.