Related papers: On the Conditional Distribution of the Multivariat…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

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…

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…

Factor Analysis based on multivariate $t$ distribution ($t$fa) is a useful robust tool for extracting common factors on heavy-tailed or contaminated data. However, $t$fa is only applicable to vector data. When $t$fa is applied to matrix…

The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…

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…

Markov switching models are often used to analyze financial returns because of their ability to capture frequently observed stylized facts. In this paper we consider a multivariate Student-t version of the model as a viable alternative to…

Abel-Tauberian theorems relate power law behavior of distributions and their transforms. We formulate and prove a multivariate version for non-standard regularly varying measures on $\mathbb{R}_+^p$ and then apply it to prove that the joint…

Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…

One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also…

Multivariate Poisson distributions have numerous applications. Fast computation of these distributions, holding constant a fixed set of linear combinations of these variables, has been explored by Sontag and Zeilberger. This elaborates on…

The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…

Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…

Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

We consider turbulent advection of a scalar field $T(\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $\Delta T(R)$ across a scale $R$. In particular we focus on two conditional…

We propose a modified weighted Nadaraya-Watson estimator for the conditional distribution of a time series with heavy tails. We establish the asymptotic normality of the proposed estimator. Simulation study is carried out to assess the…