Related papers: A complete data frame work for fitting power law d…

Many objects studied in astronomy follow a power law distribution function, for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

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…

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…

How to estimate the uncertainty of a given model is a crucial problem. Current calibration techniques treat different classes equally and thus implicitly assume that the distribution of training data is balanced, but ignore the fact that…

Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…

This article describes a methodology for fitting experimental data to the discrete power-law distribution and provides the results of a detailed simulation exercise used to calculate accurate cutoff values used to assess the fit to a…

Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by…

We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…

Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…

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…

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…

We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood…

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…

Heavy-tailed phenomena appear across diverse domains --from wealth and firm sizes in economics to network traffic, biological systems, and physical processes-- characterized by the disproportionate influence of extreme values. These…

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…