Related papers: Bimatrix variate generalised beta distributions
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…
A multivariate extension of the Dickman distribution was recently introduced, but very few properties have been studied. We discuss several properties with an emphasis on simulation. Further, we introduce and study a multivariate extension…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
We present in this paper the theory of multivariate Banach spaces of random variables with exponential decreasing tails of distributions.
A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new…
Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…
We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the "beta ensembles") are described by the spectrum of a random diffusion generator. By a Riccati…
Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then…
We discuss invariants in equivariant birational geometry.
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
In random matrix theory, the spectral distribution of the covariance matrix has been well studied under the large dimensional asymptotic regime when the dimensionality and the sample size tend to infinity at the same rate. However, most…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…
We extend the results about the fluctuations of the matrix entries of regular functions of Wigner matrices to the case of sample covariance random matrices.
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005). We refer to this new distribution as bivariate gamma-geometric (BGG) law. A bivariate random vector…
Recently, Lee and Cha (2015, `On two generalized classes of discrete bivariate distributions', {\it American Statistician}, 221 - 230) proposed two general classes of discrete bivariate distributions. They have discussed some general…
We provide optimal bounds for $\alpha (\beta \circ \gamma \circ \dots )$ in $4$-distributive varieties, as well as some further partial generalizations.
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…