Related papers: Distributions of missing sums and differences
In this paper, we study the sum of the divisor function over sets with digit restrictions.
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Certain new inequalities for the sums of factorials are presented.
Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it…
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
For any finite set of integers X, define its sumset X+X to be {x+y: x, y in X}. In a recent paper, Martin and O'Bryant investigated the distribution of |A+A| given the uniform distribution on subsets A of {0, 1, ..., n-1}. They also…
The purpose of this paper is to provide a random version of Simons' inequality.
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss.…
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose…
These informal notes are concerned with sums and averages in various situations in analysis.
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
In this paper, we consider certain finite sums related to the "largest odd divisor", and we obtain, using simple ideas and recurrence relations, sharp upper and lower bounds for these sums.
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.
We study sums of arithmetic functions, defined on Gaussian integers and taken over those pairs of integers whose coordinates give rise to a singular system.
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.