Related papers: Heavy-tailed probability distributions in social s…
It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths…
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…
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…
We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In…
The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to 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…
The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
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…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most…
Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers…
We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the…
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…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…
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…