A geometric derivation of the Irwin-Hall distribution
type: Item
instance of: scholarly article
title: A geometric derivation of the Irwin-Hall distribution
zbMATH Open document ID: 1412.60030
DOI: 10.1155/2017/3571419
author: James E. Marengo
author: David L. Farnsworth
author: Lucas Stefanic
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2018-05-25T00:00:00Z
review text: Summary: The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution's history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length. The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 6873339
zbMATH Keywords: Irwin-Hall distribution
zbMATH Keywords: inclusion-exclusion principle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3571419
OpenAlex ID: W2754974146
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description: scientific article; zbMATH DE number 6873339