Related papers: Discrete Gaussian distributions via theta function…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds…
We introduce a new Tauberian framework through the theory of "regular arithmetic functions". This allows us to establish a characterization of the Riemann hypothesis by linking the floor function to the distribution of nontrivial zeros of…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
The direct Gaussian copula model with discrete marginal distributions is an appealing data-analytic tool but poses difficult computational challenges due to its intractable likelihood. A number of approximations/surrogates for the…
Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include…
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…
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…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test…
Analyzing in detail the analytic continuation of the Riemann zeta function we are able to generate several new identities which may be useful for application in physics and mathematics.
We study the asymptotic laws for the spatial distribution and the number of connected components of zero sets of smooth Gaussian random functions of several real variables. The primary examples are various Gaussian ensembles of real-valued…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
In 2002 Freiberg and Z\"ahle introduced and developed a harmonic calculus for measure-geometric Laplacians associated to continuous distributions. We show their theory can be extended to encompass distributions with finite support and give…
Riemann's non-differentiable function and Gauss's quadratic reciprocity law have attracted the attention of many researchers. In \cite{RM} Murty and Pacelli gave an instructive proof of the quadratic reciprocity via the theta-transformation…
Tweedie's formula is central to measurement-error analysis and empirical Bayes. Under Gaussian noise, the formula identifies the posterior mean directly from the observed-data density, bypassing nonparametric deconvolution. Beyond a few…