The Three Sigma Rule
Open accessAbstract
For random variables with a unimodal Legesgue density, the 3[sgrave] rule is proved by elementary calculus. It emerges as a special case of the Vysochanskiĭ-Petunin inequality, which in turn is based on the Gauss inequality.
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- Authors
- Pukelsheim, F.
- Affiliations
- University of Augsburg (DE)
- Corresponding author
- Pukelsheim, Friedrich
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1994-05
- Volume
- 48
- Issue
- 2
- Pages
- 88-91
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2079054072
- Cited by
- 1,242
- References
- 0
- Citations by year
- 2026: 69 · 2025: 95 · 2024: 112 · 2023: 130 · 2022: 100 · 2021: 85 · 2020: 111 · 2019: 96 · 2018: 68 · 2017: 54 · 2016: 45 · 2015: 43 · 2014: 39 · 2013: 32 · 2012: 31
- FWCI
- 2.65
- Type
- journal article
- Language
- en
- Open access
- Locations
- The American Statistician (publishedVersion)
- OPUS (Augsburg University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- three-sigma rule, unimodal distributions, Lebesgue density, probability bounds, normal distribution
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