Subexponential distribution (light-tailed)


In probability theory, one definition of a subexponential distribution is as a probability distribution whose tails decay at an exponential rate, or faster: a real-valued distribution is called subexponential if, for a random variable,
The subexponential norm,, of a random variable is defined by
This is an example of a Orlicz norm. An equivalent condition for a distribution to be subexponential is then that
Subexponentiality can also be expressed in the following equivalent ways:
  1. for all and some constant.
  2. for all and some constant.
  3. For some constant, for all.
  4. exists and for some constant, for all.
  5. is sub-Gaussian.