Related papers: Heavy-tailed Distributions In Stochastic Dynamical…
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…
Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of…
We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…
Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…
The areas under workload process and under queuing process in a single server queue over the busy period have many applications not only in queuing theory but also in risk theory or percolation theory. We focus here on the tail behaviour of…
With the rise of computing and artificial intelligence, advanced modeling and forecasting has been applied to High Frequency markets. A crucial element of solid production modeling though relies on the investigation of data distributions…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
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…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
We study inelastic gases in two dimensions using event-driven molecular dynamics simulations. Our focus is the nature of the stationary state attained by rare injection of large amounts of energy to balance the dissipation due to…
Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…
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…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…
In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…
We introduce a new family of multivariate distributions by taking the component-wise Tukey-h transformation of a random vector following a skew-normal distribution. The proposed distribution is named the skew-normal-Tukey-h distribution and…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
Heavy-tailed fluctuations and power law statistics pervade physics, finance, and economics, yet their origin is often ascribed to systems poised near criticality. Here we show that such behavior can emerge far from instability through a…
Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing…
In the liquefied natural gas (LNG) shipping industry, the phenomenon of sloshing can lead to the occurrence of very high pressures in the tanks of the vessel. The issue of modelling or estimating the probability of the simultaneous…