Analyzing Zipf’s Law: Reflections on Power Law or Sigmoid Distribution

The Urban hierarchy has often been explained with Zipf’s law, a par-ticular form of the power law where the shape parameter tends to equal 1. There is a large literature on the applicability of Zipf’s law to different spatial and his-torical contexts, which is generally valid but not optimal. In fact, there is a wide debate about whether the mathematical form expressed by Zipf’s Law is the best distribution to represent urban hierarchies since this function seems to decline in its ability to represent the “fat tail” of the distribution curve. The objective of this study is to show there is a distribution function potentially better than Zipf that is based on a sigmoid function. This particular function represents the hierarchy between urban centers, even the smallest ones, in a much more accurate way. The use of this function overcomes the problems arising when adopting a Pareto func-tion-which is valid only for the group of major cities-either a log-normal one or a combination of both. The sigmoid function has been applied to a sample of European countries, showing constant application validity.