A Geometric Derivation of the Irwin-Hall Distribution
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 approxima...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2017/3571419 |
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| author | James E. Marengo David L. Farnsworth Lucas Stefanic |
| author_facet | James E. Marengo David L. Farnsworth Lucas Stefanic |
| author_sort | James E. Marengo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c11b0951b4c949cb9637947fefcae510 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c11b0951b4c949cb9637947fefcae5102025-02-03T01:21:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252017-01-01201710.1155/2017/35714193571419A Geometric Derivation of the Irwin-Hall DistributionJames E. Marengo0David L. Farnsworth1Lucas Stefanic2School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USASchool of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USASchool of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USAThe 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.http://dx.doi.org/10.1155/2017/3571419 |
| spellingShingle | James E. Marengo David L. Farnsworth Lucas Stefanic A Geometric Derivation of the Irwin-Hall Distribution International Journal of Mathematics and Mathematical Sciences |
| title | A Geometric Derivation of the Irwin-Hall Distribution |
| title_full | A Geometric Derivation of the Irwin-Hall Distribution |
| title_fullStr | A Geometric Derivation of the Irwin-Hall Distribution |
| title_full_unstemmed | A Geometric Derivation of the Irwin-Hall Distribution |
| title_short | A Geometric Derivation of the Irwin-Hall Distribution |
| title_sort | geometric derivation of the irwin hall distribution |
| url | http://dx.doi.org/10.1155/2017/3571419 |
| work_keys_str_mv | AT jamesemarengo ageometricderivationoftheirwinhalldistribution AT davidlfarnsworth ageometricderivationoftheirwinhalldistribution AT lucasstefanic ageometricderivationoftheirwinhalldistribution AT jamesemarengo geometricderivationoftheirwinhalldistribution AT davidlfarnsworth geometricderivationoftheirwinhalldistribution AT lucasstefanic geometricderivationoftheirwinhalldistribution |