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Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…

Machine Learning · Computer Science 2011-03-22 Danny Bickson , Carlos Guestrin

We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model…

High Energy Physics - Theory · Physics 2016-05-31 Takuya Kanazawa

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…

Statistics Theory · Mathematics 2014-04-10 Stéphan Clémençon , Antoine Dematteo

We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…

Methodology · Statistics 2019-01-25 Dexter Cahoy , Joseph Sedransk

We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed…

Methodology · Statistics 2023-05-09 Esa Ollila , Daniel P. Palomar , Frederic Pascal

We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…

Statistics Theory · Mathematics 2019-12-10 Farzad Pourbabaee , Omid Shams Solari

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…

Probability · Mathematics 2025-06-18 Yuyu Chen , Seva Shneer

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

Computation · Statistics 2019-09-30 Rui Zhou , Junyan Liu , Sandeep Kumar , Daniel P. Palomar

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…

Mathematical Physics · Physics 2011-05-09 Ph. Blanchard , T. Krueger , D. Volchenkov

Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…

Statistical Mechanics · Physics 2020-02-26 Maike A. F. dos Santos

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…

Statistics Theory · Mathematics 2024-05-01 Kai Wang , Chengxiu Ling

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…

Populations and Evolution · Quantitative Biology 2025-09-23 Luis F. Gordillo , Priscilla E. Greenwood

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…

Risk Management · Quantitative Finance 2023-04-12 Bikramjit Das , Vicky Fasen-Hartmann

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…

Methodology · Statistics 2023-10-19 Sagnik Mondal , Marc G. Genton

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

Risk Management · Quantitative Finance 2020-01-14 Xing Yan , Qi Wu , Wen Zhang

Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative…

Probability · Mathematics 2019-01-21 Harry Joe , Haijun Li

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

Probability · Mathematics 2016-05-10 Anja Janßen , Thomas Mikosch , Mohsen Rezapour , Xiaolei Xie

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

Probability · Mathematics 2021-02-17 Elvira Di Nardo , Federico Polito , Enrico Scalas

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Statistics Theory · Mathematics 2013-12-20 J. L. Wadsworth , J. A. Tawn

We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default…

Risk Management · Quantitative Finance 2016-07-19 Jianxi Su , Edward Furman