Related papers: A Rank-Based Approach to Zipf's Law
Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated.…
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…
Using the theory of Dirichlet forms we construct a large class of continuous semimartingales on an open domain $E \subset \mathbb{R}^d$, which are governed by rank-based, in addition to name-based, characteristics. Using the results of Baur…
In the double rank analysis of research publications, the local rank position of a country or institution publication is expressed as a function of the world rank position. Excluding some highly or lowly cited publications, the double rank…
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…
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 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 joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a…
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…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
The growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is…
In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In…
We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple…
A money-based model for the power law distribution (PLD) of wealth in an economically interacting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro…
We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the…
Ranking lists are often provided at regular time intervals in a range of applications, including economics, sports, marketing, and politics. Most popular methods for rank-order data postulate a linear specification for the latent scores,…
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics is offering models of markets as complex systems, such as the gas-like model, able to predict money distributions…
We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii)…
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…