Related papers: Non-parametric power-law surrogates
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…
The method of constrained randomisation is applied to three-dimensional simulated galaxy distributions. With this technique we generate for a given data set surrogate data sets which have the same linear properties as the original data…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
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…
This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions.…
Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many…
The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear…
Over the last decades, impressive progresses have been made in many experimental domains, e.g. microscopic techniques such as single-particle tracking, leading to plethoric amounts of data. In a large variety of systems, from natural to…
In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme…
Many experimental quantities show a power-law distribution $p(x)\propto x^{-\alpha}$. In astrophysics, examples are: size distribution of dust grains or luminosity function of galaxies. Such distributions are characterized by the exponent…
Many natural processes exhibit power-law behavior. The power-law exponent is linked to the underlying physical process and therefore its precise value is of interest. With respect to the energy content of nanoflares, for example, a…
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…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of worldwide stock markets indexes data and it has the form $Pr(X>x) ~ x**(-alpha) for…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
Hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realization of a linear stochastic process. Typically, this is done by generating surrogates which are made to conform to…
The surrogate data method is widely applied as a data dependent technique to test observed time series against a barrage of hypotheses. However, often the hypotheses one is able to address are not those of greatest interest, particularly…