Related papers: A classification of the natural and social distrib…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
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…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
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…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
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…
Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…
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 review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
More than one billion data sampled with different frequencies from several financial instruments were investigated with the aim of testing whether they involve power law. As a result, a known power law with the power exponent around -4 was…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
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.…
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…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…