Related papers: Sums of Standard Uniform Random Variables
The distribution function of a random distance in three dimensions is given and some new three-dimensional d2-tests of randomness are suggested. We show that our test statistics are not correlated with the usual test statistics and are…
We prove that the probability that a sum of independent random variables in $\mathbb{R}^d$ with bounded densities lies in a ball is maximized by taking uniform distributions on balls. This in turn generalizes a result by Rogozin on the…
This paper investigates the Erd\H{o}s distinct subset sums problem in $\mathbb{Z}^k$. Beyond the classical variance method, using alternative statistical quantities like $\mathbb{E}[\|X\|_1]$ and $\mathbb{E}[\|X\|_3^3]$ can yield better…
We study the problem of estimating the sum of $n$ elements, each with weight $w(i)$, in a structured universe. Our goal is to estimate $W = \sum_{i=1}^n w(i)$ within a $(1 \pm \epsilon)$ factor using a sublinear number of samples, assuming…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…
The complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…