Related papers: Non-parametric power-law surrogates
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
Power-law distributions contain precious information about a large variety of processes in geoscience and elsewhere. Although there are sound theoretical grounds for these distributions, the empirical evidence in favor of power laws has…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are close). The proposed method represents the likelihood…
Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…
This paper considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…
One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means…
Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the…
This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
Distinguishing power-law distributions from other heavy-tailed distributions is challenging, and this task is often further complicated by subsampling effects. In this work, we evaluate the performance of two commonly used methods for…