Related papers: Power-law distributions in empirical data
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution…
Selected examples of possible origins of power-law distributions are presented.
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
In filtering, each output is produced by a certain number of different inputs. We explore the statistics of this degeneracy in an explicitly treatable filtering problem in which filtering performs the maximal compression of relevant…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
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…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
In recent years, power analysis has become widely used in applied sciences, with the increasing importance of the replicability issue. When distribution-free methods, such as Partial Least Squares (PLS)-based approaches, are considered,…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
The analysis of Tables of particle properties shows that the probability distribution of the results of physical measurements is far from the conventional Gaussian $\rho(\xi)=exp(-\xi^2/2) $, but is more likely to follow the simple…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…
We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…
Building on the theoretical insights of Part I, this paper, as the second part of the tutorial, dives deeper into data-driven power flow linearization (DPFL), focusing on comprehensive numerical testing. The necessity of these simulations…
We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset…
We show how recent results by Bening and Korolev in the context of estimation, when linked with a classical result of Fisher concerning the negative binomial distribution, can be used to explain the ubiquity of power law probability…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…
Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…