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:
References
Sub-Gaussian distribution Wikipedia(Text) CC BY-SA