A Geometric Derivation of the Irwin-Hall Distribution
Joint Authors
Marengo, James E.
Stefanic, Lucas
Farnsworth, David L.
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-18
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Marengo, James E.& Farnsworth, David L.& Stefanic, Lucas. 2017. A Geometric Derivation of the Irwin-Hall Distribution. International Journal of Mathematics and Mathematical Sciences،Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1167720
Modern Language Association (MLA)
Marengo, James E.…[et al.]. A Geometric Derivation of the Irwin-Hall Distribution. International Journal of Mathematics and Mathematical Sciences No. 2017 (2017), pp.1-6.
https://search.emarefa.net/detail/BIM-1167720
American Medical Association (AMA)
Marengo, James E.& Farnsworth, David L.& Stefanic, Lucas. A Geometric Derivation of the Irwin-Hall Distribution. International Journal of Mathematics and Mathematical Sciences. 2017. Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1167720
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1167720