Definition:Sub-Exponential Distribution
Jump to navigation
Jump to search
Definition
The distribution of a random variable $X$ with expectation $\mu = \expect X$ is called sub-exponential if and only if there exists $\nu\in \R_{> 0}, \alpha \in \R_{\ge 0}$ such that:
- $\expect {e^{\lambda \paren {X - \mu} } } \le e^{\nu^2 \lambda^2 / 2}$
for all $\size \lambda < \dfrac 1 \alpha$.
This article, or a section of it, needs explaining. In particular: Where does $\alpha$ come into it? You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Basic Properties
This page or section has statements made on it that ought to be extracted and proved in a Theorem page. In particular: according to house style -- this as a result reported in an "Also see" section You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by creating any appropriate Theorem pages that may be needed. To discuss this page in more detail, feel free to use the talk page. |
The sub-Gaussian distribution results as a special case ($\nu = \sigma, \alpha = 0$).