Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution equation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. ...

Fallout mass-size distributions presently used at USNRDL are compared vith new distributions suggested by recent investigations. Available data is unable to define the distribution parameters well enough to distinguish between lognormal and power-law distribution models.,

Bayesian modelling and statistical text analysis rely on informed probability priors to encourage good solutions. This paper empirically analyses whether in medical discharge reports follow Zipf’s law, a commonly assumed property of language where word frequency follows discrete power-law distribution. We examined 20,000 from the MIMIC-III dataset. Methods included splitting into tokens, counti...

A recently proposed unified scaling law for interoccurrence times of earthquakes is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the nonstationarity of the process, show a double power-...

It has been suggested that frequency distributions of individual tree masses in natural stands are characterized by power-law distributions with exponents near -3/4, and that therefore tree communities exhibit energetic equivalence among size classes. Because the mass of trees is not measured directly, but estimated from diameter, this supposition is based on the fact that the observed distribu...

Power law distributions have been repeatedly observed in a wide variety of socioeco-nomic, biological and technological areas, including distributions of: wealth, species-arearelationships, populations of cities, values of companies, sizes of living organisms and, morerecently, documents and visitors on the Web, etc. In the vast majority of these observa-tions, e.g., city po...

Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal distributions fit better than the power law and negative binomial distributions, no comparisons so far have covered all articles within a discipline, including those ...

We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s for any s . We apply our results to networks with the three most commonly studied degree distributions-Poisson, exponential, and power-law-as well as to the calculatio...

Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions for situations in which a "joiner particle" k pays some form of price to enter a community of size , where costs are subject to economies of scale. Maximizing the Boltzmann-Gibbs-Shann...

For taxonomic levels higher than species, the abundance distributions of the number of subtaxa per taxon tend to approximate power laws but often show strong deviations from such laws. Previously, these deviations were attributed to finite-time effects in a continuous-time branching process at the generic level. Instead, we describe herein a simple discrete branching process that generates the ...