Related papers: Distributional Point Values and Delta Sequences

In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…

We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…

We introduce a new notion of generalization -- Distributional Generalization -- which roughly states that outputs of a classifier at train and test time are close *as distributions*, as opposed to close in just their average error. For…

We give a survey of the use of infinitesimals within mathematical analysis to rigorously deal with the delta-function from physics, and more generally, with distributions in the sense of L. Schwartz. We use the framework of nonstandard…

This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

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…

In this paper, we first generalize a value distribution result of Lahiri and Dewan [4] and as an application of this result we prove a normality criterion using partial sharing of small functions. Further, in sequel normality criteria of Hu…

Let $\{X_n,n\ge1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...,X_{n-1}\}+\delta$, where $\delta$ is an integer…

We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…

Distributional semantics has had enormous empirical success in Computational Linguistics and Cognitive Science in modeling various semantic phenomena, such as semantic similarity, and distributional models are widely used in…

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…

We introduce the concept of $\delta$-sequence. A $\delta$-sequence $\Delta$ generates a well-ordered semigroup $S$ in $\mathbb{Z}^2$ or $\mathbb{R}$. We show how to construct (and compute parameters) for the dual code of any evaluation code…

In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions…

We investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible…

Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…

We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.

In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…

It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges. We prove a limit law…

This paper focuses on the convergence of infor- mation in distributed systems of agents communicating over a network. The information on which the convergence is sought is not represented by real numbers, rather by sets of real numbers,…