Related papers: MetaZipf. (Re)producing knowledge about city size …
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a…
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as…
The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail,…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
Stochastic equations constitute a major ingredient in many branches of science, from physics to biology and engineering. Not surprisingly, they appear in many quantitative studies of complex systems. In particular, this type of equation is…
Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the…
Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model…
We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics
With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been…
We study rank-size distribution of cities in Japan on the basis of data analysis. From the census data after World War II, we find that the rank-size distribution of cities is composed of two parts, each of which has independent power…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…