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Power-Law Distributions in Empirical Data [PDF]
SIAM Review, 2009 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/
Mark Newman +2 more
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Power Law Distributions in Information Retrieval
ACM Transactions on Information Systems, 2016Several properties of information retrieval (IR) data, such as query frequency or document length, are widely considered to be approximately distributed as a power law. This common assumption aims to focus on specific characteristics of the empirical probability distribution of such data (e.g., its scale-free nature or its long/fat tail).
Casper Petersen +2 more
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Stability and relaxation of power-law distribution
Physical Review A, 1990We study the stability of the steady state in an aggregation system with injection for one dimension and the mean-field cases. We prove that for any initial perturbation the system is stable and eventually recovers the power-law steady state. The form of the relaxation follows either a stretched exponential (${\mathit{e}}^{\mathrm{\ensuremath ...
Hideki Takayasu +2 more
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Discrete Truncated Power‐Law Distributions
Australian & New Zealand Journal of Statistics, 2016SummaryDiscrete power‐law distributions have significant consequences for understanding many phenomena in practice, and have attracted much attention in recent decades. However, in many practical applications, there exists a natural upper bound for the probability tail. In this paper, we develop maximum likelihood estimates for truncated discrete power‐
Zhu, Hong, Xie, Yingchao, Xu, Maochao
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2000
Summing N i.i.d. random variables with pdf P l(x), one obtains a random variable which has in general a different pdf P N(x) given by N convolutions of P1(x) with itself as given by (2.62).
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Summing N i.i.d. random variables with pdf P l(x), one obtains a random variable which has in general a different pdf P N(x) given by N convolutions of P1(x) with itself as given by (2.62).
openaire +1 more source
Power Laws and Skew Distributions
Communications in Computational Physics, 2012Power-law distributions and other skew distributions, observed in various models and real systems, are considered. A model, describing evolving systems with increasing number of elements, is considered to study the distribution over element sizes. Stationary power-law distributions are found.
Reinhard Mahnke +2 more
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