Related papers: Rank Distributions: Frequency vs. Magnitude
In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its…
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…
Beta Rank Function (BRF) is a two-sided distribution characterized by a smooth peak and double powerlaw decay, widely used to model empirical data exhibiting deviations from pure power laws. In this paper, we introduce a novel two-step…
Causal processes can give rise to distinctive distributions in the linguistic variables that they affect. Consequently, a secure understanding of a variable's distribution can hold a key to understanding the forces that have causally shaped…
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…
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…
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is…
The value of a social network is generally determined by its size and the connectivity of its nodes. But since some of the nodes may be fake ones and others that are dormant, the question of validating the node counts by statistical tests…
We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a…
It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
Zipf's law implies the statistical distributions of hyperbolic type, which can describe the properties of stability and entropy loss in linguistics. We present the information theory from which follows that if the system is described by…
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…
The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$. Previous work has stressed that this pattern arises from…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
We investigate the average sizes of the $n$ largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte…
Discovery of a new scale-free law of earthquake phenomenon is reported. It is relevant to the structural and dynamical properties of the earthquake network proposed in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)].…
Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…
Benford's Law is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of…
This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various…