Related papers: Heavy-tails in economic data: fundamental assumpti…
We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing but locally conserving money transactions, the money distribution goes to the…
We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and…
We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
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…
Tail risk protection is in the focus of the financial industry and requires solid mathematical and statistical tools, especially when a trading strategy is derived. Recent hype driven by machine learning (ML) mechanisms has raised the…
(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
The climate change dispute is about changes over time of environmental characteristics (such as rainfall). Some people say that a possible change is not so much in the mean but rather in the extreme phenomena (that is, the average rainfall…
Climate extremes such as floods, storms, and heatwaves have caused severe economic and human losses across Europe in recent decades. To support the European Union's climate resilience efforts, we propose a statistical framework for…
Long-tailed data is a special type of multi-class imbalanced data with a very large amount of minority/tail classes that have a very significant combined influence. Long-tailed learning aims to build high-performance models on datasets with…
The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…
We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to…
An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…