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Subexponential distribution (light-tailed)

In probability theory, in the context of light-tailed distributions, one definition of a subexponential distribution is as a probability distribution whose tails decay at an exponential rate, or faster: a real-valued distribution D{\displaystyle {\cal {D}}} is called subexponential if, for a random variable X∼D{\displaystyle X\sim {\cal {D}}}, P(|X|≥x)=O(e−Kx){\displaystyle {\mathbb {P}}(|X|\geq x)=O(e^{-Kx})}, for large x{\displaystyle x} and some constant K>0{\displaystyle K>0}.Note that this is almost the opposite of the more established meaning of subexponential in the context of Heavy-tailed distributions, where "sub" means that the rate of decay is slower than exponential, rather than that the tail is lighter than exponential.

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