Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ ex-Gaussian distribution ▷ Definition

Definition: Let $A$ be a random variable that is normally distributed with mean $\mu$ and variance $\sigma^2$, and let $B$ be a random variable that is exponentially distributed with rate $\lambda$. Suppose further that $A$ and $B$ are independent. Then the sum $X=A+B$ is said to have an exponentially-modified Gaussian (i.e., ex-Gaussian) distribution, with parameters $\mu$, $\sigma$, and $\lambda$; that is,

\[\label{eq:exg} X \sim \text{ex-Gaussian}(\mu, \sigma, \lambda) \; ,\]

where $\mu \in \mathbb{R}$, $\sigma>0$, and $\lambda > 0$.


Metadata: ID: D187 | shortcut: exg | author: tomfaulkenberry | date: 2023-04-18, 12:00.