Related papers: Convolution-t Distributions
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
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…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…
We propose a flexible family of distributions, generalized $t$-distributions, on the cylinder which is obtained as a conditional distribution of a trivariate $t$ distribution. The new distribution has unimodality or bimodality, symmetry or…
A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable…
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…
Handling multiplicity without losing much power has been a persistent challenge in various fields that often face the necessity of managing numerous statistical tests simultaneously. Recently, $p$-value combination methods based on…
We develop an econometric framework integrating heavy-tailed Student's $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we…
We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized…