Related papers: Exploring the Statistical Properties of Outputs fr…
We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse…
We show a statistical version of Taylor's theorem and apply this result to non-parametric density estimation from truncated samples, which is a classical challenge in Statistics \cite{woodroofe1985estimating, stute1993almost}. The…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
In [3], algorithms to compute the density of the distance to a random variable uniformly distributed in (a) a ball, (b) a disk, (c) a line segment, or (d) a polygone were introduced. For case (d), the algorithm, based on Green's theorem,…
The center of gravity is one of the most frequently used algorithm for position reconstruction with different analytical forms for the noise optimization. The error distributions of the different forms are essential instruments to improve…
The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
Consider the Erd\H{o}s-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring…
We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the {\em special endogenous solution} to a stochastic fixed-point…
Goodness-of-fit tests gauge whether a given set of observations is consistent (up to expected random fluctuations) with arising as independent and identically distributed (i.i.d.) draws from a user-specified probability distribution known…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…