Related papers: A universal rank-size law
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
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…
As the most fundamental empirical law, Zipf's law has been studied from many aspects. But its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a new concept named nonsymmetric entropy…
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…
This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
Many scientists are interested in but puzzled by the various inverse power laws with a negative exponent 1 such as the rank-size rule. The rank-size rule is a very simple scaling law followed by many observations of the ubiquitous empirical…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…
We summarize a book under publication with his title written by the three present authors, on the theory of Zipf's law, and more generally of power laws, driven by the mechanism of proportional growth. The preprint is available upon request…
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…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European…
We consider a two-parameter discrete generalized beta (DGB) distribution and propose its universal applications to study the size-distribution of the urban agglomerations across various countries in the world, where the urban agglomerations…
Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions…
This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
We study the distribution of neighborhoods across a set of 12 global cities and find that the distribution of neighborhood sizes follows exponential decay across all cities under consideration. We are able to analytically show that this…
The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…