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Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Fat tailed statistics and power-laws are ubiquitous in many complex systems. Usually the appearance of of a few anomalously successful individuals (bio-species, investors, websites) is interpreted as reflecting some inherent "quality"…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…
Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…
Power law distributions, in particular Pareto distributions, describe data across diverse areas of study. We have developed a package in R to estimate the tail index for such datasets focusing on speed (in particular with large datasets),…
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 $\{p_k\}$ for situations in…
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…
The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
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…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers…