The Three Sigma Rule

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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Bibliographic Details
Published in:The American statistician 1994-05, Vol.48 (2), p.88-91
Main Author: Pukelsheim, Friedrich
Format: Article
Language:English
Subjects:
Bienaymé-Chebyshev inequality
Calculus
Convexity
Distribution functions
Distribution theory
Exact sciences and technology
Gauss inequality
Mathematical functions
Mathematical inequalities
Mathematics
Probabilities
Probability and statistics
Probability theory
Probability theory and stochastic processes
Random variables
Rectangles
Sciences and techniques of general use
Statistics
Vysochanskiĭ-Petunin inequality
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Description
Summary: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.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.1994.10476030