Related papers: The envelope of a complex Gaussian random variable
The entropy computation of Gaussian mixture distributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
The entropy per coordinate in a log-concave random vector of any dimension with given density at the mode is shown to have a range of just 1. Uniform distributions on convex bodies are at the lower end of this range, the distribution with…
This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
We consider the moment space $\mathcal{M}_n$ corresponding to $p \times p$ real or complex matrix measures defined on the interval $[0,1]$. The asymptotic properties of the first $k$ components of a uniformly distributed vector $(S_{1,n},…
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a particular type of norm on $\mathbb{R}^d$, called $D$-norm. The…
We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we…
Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…
The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
Two- and three-particle distribution amplitudes of heavy pseudoscalar mesons of well-defined geometric twist are introduced. They are obtained from appropriately parametrized vacuum-to-meson matrix elements by applying those twist…
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for…
A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring…