Related papers: Snooker Statistics and Zipf's Law
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…
We study rank-frequency relations for phonemes, the minimal units that still relate to linguistic meaning. We show that these relations can be described by the Dirichlet distribution, a direct analogue of the ideal-gas model in statistical…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
In this paper we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all…
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…
The text-length-dependence of real word-frequency distributions can be connected to the general properties of a random book. It is pointed out that this finding has strong implications, when deciding between two conceptually different views…
Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and…
The random Fibonacci chain is a generalisation of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1 \mapsto 01$ with probability $p$ and $1 \mapsto 10$ with probability $1-p$ for $0<p<1$ and where…
Zipf's law states that the probability of a variable being larger than $s$ is roughly inversely proportional to $s$. In this paper, we evaluate Zipf's law for the distribution of firm size by the number of employees in Brazil. We use…
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…
Virtually anything can be and is ranked; people, institutions, countries, words, genes. Rankings reduce complex systems to ordered lists, reflecting the ability of their elements to perform relevant functions, and are being used from…
In this work we study a modified version of the two-dimensional Sznajd sociophysics model. In particular, we consider the effects of agents' reputations in the persuasion rules. In other words, a high-reputation group with a common opinion…
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two…
Despite renewed interest in emergent language simulations with neural networks, little is known about the basic properties of the induced code, and how they compare to human language. One fundamental characteristic of the latter, known as…
Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going…