Related papers: Zipf's Law for Atlas Models
The evolution of open source software projects in Linux distributions offers a remarkable example of a growing complex self-organizing adaptive system, exhibiting Zipf's law over four full decades. We present three tests of the usually…
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…
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 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…
We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an…
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…
Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on the intercontinental level. In this paper, we address this issue by creating a collection of…
This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
Following the work of Okuyama, Takayasu and Takayasu [Okuyama, Takayasu and Takayasu 1999] we analyze huge databases of Japanese companies' financial figures and confirm that the Zipf's law, a power law distribution with the exponent -1,…
Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global…
We introduce an auto-regressive model which captures the growing nature of realistic markets. In our model agents do not trade with other agents, they interact indirectly only through a market. Change of their wealth depends, linearly on…
The distribution of income and wealth in developed economies exhibits a robust two-class structure: an exponential (Boltzmann--Gibbs) bulk covering $\sim\!97\%$ of the population, and a power-law (Pareto) tail in the upper $\sim\!3\%$. We…
The nature of the quantitative distribution of the 64 DNA codons in the human genome has been an issue of debate for over a decade. Some groups have proposed that the quantitative distribution of the DNA codons ordered as a rank-frequency…
The distribution of wealth in the Hungarian medieval aristocratic society is reported and studied. The number of serf families belonging to a noble is taken as a measure of the corresponding wealth. Our results reveal the power-law nature…
Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper…