Related papers: Beyond Zipf's Law: The Lavalette Rank Function and…

Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…

The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…

Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…

Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…

Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…

In this paper we will look at the distribution with which passwords are chosen. Zipf's Law is commonly observed in lists of chosen words. Using password lists from four different on-line sources, we will investigate if Zipf's law is a good…

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…

The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…

A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon…

We address the general problem of testing a power law distribution versus a log-normal distribution in statistical data. This general problem is illustrated on the distribution of the 2000 US census of city sizes. We provide definitive…

Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers…

Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…

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…

Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation.…

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…

This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent…

The article introduces corrections to Zipf's and Heaps' laws based on systematic models of the proportion of hapaxes, i.e., words that occur once. The derivation rests on two assumptions: The first one is the standard urn model which…

English words and the outputs of many other natural processes are well-known to follow a Zipf distribution. Yet this thoroughly-established property has never been shown to help compress or predict these important processes. We show that…

The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are…

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…