Related papers: Description Complexity of Regular Distributions

We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…

Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the…

We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the…

In this short note, we present a refined approximation for the log-ratio of the density of the von Mises$(\mu,\kappa)$ distribution (also called the circular normal distribution) to the standard (linear) normal distribution when the…

Mixture distributions arise in many application areas, for example as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions $\mathbf p, \mathbf q$ on $\mathbb R^d$, we want to distinguish…

Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…

Motivated by questions in number theory, Myerson asked how small the sum of 5 complex nth roots of unity can be. We obtain a uniform bound of O(n^{-4/3}) by perturbing the vertices of a regular pentagon, improving to O(n^{-7/3}) infinitely…

The measurement of dispersion is one of the most fundamental and ubiquitous statistical concepts, in both applied and theoretical contexts. For dispersion measures, such as the standard deviation, to effectively capture the variability of a…

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…

The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of…

The mean density of a random closed set $\Theta$ in $\R^d$ with Hausdorff dimension $n$ is the Radon-Nikodym derivative of the expected measure $\E[\h^n(\Theta\cap\cdot)]$ induced by $\Theta$ with respect to the usual $d$-dimensional…

This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve uniform H\"{o}lder regularity in terms of $L^p$-bound on the…

For a class of McKean-Vlasov stochastic differential equations with singular interactions, which include the Coulomb/Riesz/Biot-Savart kernels as typical examples (Examples 2.1 and 2.2), we derive the well-posedness and regularity estimates…

We study the regularity of a distributional solution $(u,p)$ of the 3D incompressible evolution Navier-Stokes equations. Let $B_r$ denote concentric balls in $\mathbb{R}^3$ with radius $r$. We will show that if $p\in L^{m} (0,1; L^1(B_2))$,…

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…

We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…