相关论文: A Note on the Existence of the Multivariate Gamma …
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…
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…
Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…
A mixture of variance-gamma distributions is introduced and developed for model-based clustering and classification. The latest in a growing line of non-Gaussian mixture approaches to clustering and classification, the proposed mixture of…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
This paper discusses the family of distributions on the Grassmannian of the linear span of r central gaussian vectors parametrized by the covariance matrix. Our main result is an existence and uniqueness criterion for the maximum likelihood…
A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…
In this paper, we extend the study of bivariate generalised beta type I and II distributions to the matrix variate case.
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
Ramachandran (1969, Theorem 8) has shown that for any univariate infinitely divisible distribution and any positive real number $\alpha$, an absolute moment of order $\alpha$ relative to the distribution exists (as a finite number) if and…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
The cozero-divisor graph of a commutative ring $R$, denoted $\Gamma'(R)$, is the graph whose vertices are the non-zero and non-unit elements of $R$, with two distinct vertices $x$ and $y$ adjacent if and only if $x \notin Ry$ and $y \notin…
Let $\|\cdot\|$ denote the minimum distance to an integer. For $0<\gamma< 1$, $\theta>0$ and $(\alpha, \beta) \in \mathbb{R} \setminus \{0\} \times \mathbb{R}$ we study when \begin{equation*} \|\alpha p^{\gamma}+\beta \|<p^{-\theta},…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it has a noncommutative complex hessian that is positive…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
We present the angular distribution of gamma rays produced by proton-proton interactions in parameterized formulae to facilitate calculations in astrophysical environments. The parameterization is derived from Monte Carlo simulations of the…
Graphical tests assess whether a function of interest departs from an envelope of functions generated under a simulated null distribution. This approach originated in spatial statistics, but has recently gained some popularity in functional…