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Related papers: Generalised matricvariate $T$-distribution

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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…

Risk Management · Quantitative Finance 2021-03-10 Baishuai Zuo , Chuancun Yin

In this paper, we develop local expansions for the ratio of the centered matrix-variate $T$ density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several…

Statistics Theory · Mathematics 2022-11-18 Frédéric Ouimet

In this article, we define a matrix variate asymmetric Laplace distribution. We prove some properties of the matrix variate asymmetric Laplace distribution. We prove the relationship between the matrix variate asymmetric Laplace…

Probability · Mathematics 2021-06-23 Yurii Yurchenko

This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…

Functional Analysis · Mathematics 2022-01-03 Hongyu He

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

A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…

Probability · Mathematics 2022-02-01 Lev Gelimson

We investigate a family of Riesz products and show that they can be regarded as diffraction measures of generalized Thue-Morse sequences, possibly over an infinite alphabet. These measures are closely related to the dynamical system arising…

Dynamical Systems · Mathematics 2025-09-29 Philipp Gohlke , Marc Kesseböhmer , Tanja I. Schindler

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…

Methodology · Statistics 2019-12-24 Geoffrey Z. Thompson , Ranjan Maitra , William Q. Meeker , Ashraf Bastawros

For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…

Statistics Theory · Mathematics 2023-09-20 Stefano Franco , Adelchi Azzalini

A random vector $X$ with representation $X=\sum_{j\geq0}A_jZ_j$ is considered. Here, $(Z_j)$ is a sequence of independent and identically distributed random vectors and $(A_j)$ is a sequence of random matrices, `predictable' with respect to…

Probability · Mathematics 2009-09-29 Henrik Hult , Gennady Samorodnitsky

We obtain multidimensional metric uniform distribution results involving sequences in ${\mathbb R}^k$ parametrized by analytic curves. Our theorems extend the classical theorems of Weyl and Koksma in a variety of ways. One of our main…

Classical Analysis and ODEs · Mathematics 2025-09-09 Vitaly Bergelson , Joel Moreira

In this paper, the densities of the doubly singular beta type I and II distributions are found, and the joint densities of their corresponding nonzero eigenvalues are provided. As a consequence, the density function of a singular inverted…

Statistics Theory · Mathematics 2009-04-15 J. A. Diaz-Garcia , R. Gutierrez-Jaimez

This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…

Statistics Theory · Mathematics 2012-10-22 Jose A. Diaz-Garcia

We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…

Statistics Theory · Mathematics 2021-05-18 Inna Gerlovina , Alan E. Hubbard

We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…

Statistics Theory · Mathematics 2011-07-06 Piotr Graczyk , Ishi Hideyuki

Twisted Toeplitz matrices constitute a generalization of Toeplitz matrices in the sense that the entries on each diagonal no longer need to be constant, but are given by the values of a continuous function on a partition of $[0,1]$. We…

Probability · Mathematics 2026-04-23 Dario Giandinoto , Boris Shapiro

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

Logic · Mathematics 2007-05-23 Joy Jacob , Sebastian George , A M Mathai

We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…

Statistics Theory · Mathematics 2014-04-18 Amadou Sarr

In the estimation of the mean matrix in a multivariate normal distribution, the generalized Bayes estimators with closed forms are provided, and the sufficient conditions for their minimaxity are derived relative to both matrix and scalar…

Statistics Theory · Mathematics 2021-08-16 Ryota Yuasa , Tatsuya Kubokawa

We give a correspondence between automorphic pairs of distributions on $\mathbb{R}$ and Dirichlet series satisfying functional equations and some additional analytic conditions. Moreover, we show that the notion of automorphic pairs of…

Number Theory · Mathematics 2020-02-27 Tadashi Miyazaki