Related papers: Locally Sampleable Uniform Symmetric Distributions
Let $u(x)$ be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathbb{N}}$ and $(u(p_n))_{n\in\mathbb{N}}$, where $p_n$ denotes…
In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
Consider a sequence $X^n$ of length $n$ emitted by a Discrete Memoryless Source (DMS) with unknown distribution $p_X$. The objective is to construct a lossless source code that maps $X^n$ to a sequence $\widehat{Y}^m$ of length $m$ that is…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which…
Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where…
We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…
We give improved and almost optimal testers for several classes of Boolean functions on $n$ inputs that have concise representation in the uniform and distribution-free model. Classes, such as $k$-junta, $k$-linear functions, $s$-term DNF,…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
In descriptive statistics, $U$-statistics arise naturally in producing minimum-variance unbiased estimators. In 1984, Serfling considered the distribution formed by evaluating the kernel of the $U$-statistics and proposed generalized…
By a classical theorem of Koksma the sequence of fractional parts $(\{x^n\})_{n \geq 1}$ is uniformly distributed for almost all values of $x$. In the present paper we obtain an exact quantitative version of Koksma's theorem, by calculating…
Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the…
We prove a stability result for general $3$-wise correlations over distributions satisfying mild connectivity properties. More concretely, we show that if $\Sigma,\Gamma$ and $\Phi$ are alphabets of constant size, and $\mu$ is a pairwise…
To each Boolean function F from {0,1}^n to itself and each point x in {0,1}^n, we associate the signed directed graph G_F(x) of order n that contains a positive (resp. negative) arc from j to i if the partial derivative of f_i with respect…
A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used…
We outline a general procedure on how to apply random positive linear operators in nonparametric estimation. As a consequence, we give explicit confidence bands and intervals for a distribution function $F$ concentrated on $[0,1]$ by means…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
In 1969, Delange has proved a general criterion for uniform distribution of additive functions. In this paper, we study the uniform distribution of a special class of polynomially-defined additive functions where the moduli is allowed to…