相关论文: Archimedes, Gauss, and Stein

The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…

We introduce the notion of a generalized complex (GC) Stein manifold and provide complete characterizations in three fundamental aspects. First, we extend Cartan's Theorem A and B within the framework of GC geometry. Next, we define…

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection…

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…

This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Given an algebraic stack with quasiaffine diagonal, we show that each G_m-gerbe comes from a central separable algebra. In other words, Taylor's bigger Brauer group equals the etale cohomology in degree two with coefficients in G_m. This…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…

A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed,…

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…

For random matrix ensembles with non-gaussian matrix elements that may exhibit some correlations, it is shown that centered traces of polynomials in the matrix converge in distribution to a Gaussian process whose covariance matrix is…

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…

Assuming Kotz-Riesz type I and II distributions and their corresponding independent Riesz distributions the associated generalised matricvariate T distributions, termed matricvariate T-Riesz distributions for real normed division algebras…

We analyze the form of the probability distribution function P_{n}^{(\beta)}(w) of the Schmidt-like random variable w = x_1^2/(\sum_{j=1}^n x^{2}_j/n), where x_j are the eigenvalues of a given n \times n \beta-Gaussian random matrix, \beta…

Discrete mixture models provide a well-known basis for effective clustering algorithms, although technical challenges have limited their scope. In the context of gene-expression data analysis, a model is presented that mixes over a finite…

We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium…

In a recent paper (Asci \textit{et al.}, 2008) it has been shown that certain random continued fractions have a density which is a product of a beta density and a hypergeometric function $_{2}F_{1}$. In the present paper we fully exploit a…