Related papers: Zipf's Law for Atlas Models
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we…
The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders.…
The statistical characterization of the distribution of visible matter in the universe is a central problem in modern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greatest…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
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,…
The uneven distribution of wealth and individual economic capacities are among the main forces which shape modern societies and arguably bias the emerging social structures. However, the study of correlations between the social network and…
Using population data of high spatial resolution for a region in the south of Europe, we define cities by aggregating individuals to form connected clusters. The resulting cluster-population distributions show a smooth decreasing behavior…
The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the…
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…
The scale-free power-law behavior of the statistics of the download frequency of publications has been, for the first time, reported. The data of the download frequency of publications are taken from a well-constructed web page in the field…
Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech.…
We present a simple structure based model of how words are formed from morphemes. The model explains two major empirical facts: the typical distribution of word lengths and the appearance of Zipf like rank frequency curves. In contrast to…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…
We analyze three sets of income data: the US Panel Study of Income Dynamics PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with…
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…
Zipf-like distributions characterize a wide set of phenomena in physics, biology, economics and social sciences. In human activities, Zipf-laws describe for example the frequency of words appearance in a text or the purchases types in…
Financial markets display scale-free behavior in many different aspects. The power-law behavior of part of the distribution of individual wealth has been recognized by Pareto as early as the nineteenth century. Heavy-tailed and scale-free…