- Equivalent properties
- See also
- References
In probability theory, a sub-Gaussian distribution is a probability distribution with strong tail decay property. Informally, the tails of a sub-Gaussian distribution are dominated by (i.e. decay at least as fast as) the tails of a Gaussian.
Formally, the probability distribution of a random variable X is called sub-Gaussian if there are positive constants C, v such that for every t > 0,
The sub-Gaussian random variables with the following norm form a Birnbaum–Orlicz space:
Equivalent properties
The following properties are equivalent:
- The distribution of X is sub-Gaussian
-
- Laplace transform condition:
- Moment condition:
- Union bound condition:
where 
are i.i.d copies of X.
See also
- Platykurtic distribution
References
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|year=1980
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| title=Smallest singular value of random matrices and geometry of random polytopes
| journal=Adv. Math.
| volume=195
| pages=491–523
| year=2005
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| first1=Mark | last1=Rudelson
| first2=Roman | last2=Vershynin
| title=Non-asymptotic theory of random matrices: extreme singular values
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| journal=Unpublished
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1 : Continuous distributions
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