Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Wald distribution ▷ Definition

Definition: Let $X$ be a random variable. Then, $X$ is said to follow a Wald distribution with drift rate $\gamma$ and threshold $\alpha$

$\label{eq:wald} X \sim \mathrm{Wald}(\gamma, \alpha) \; ,$

if and only if its probability density function is given by

$\label{eq:wald-pdf} \mathrm{Wald}(x; \gamma, \alpha) = \frac{\alpha}{\sqrt{2\pi x^3}}\exp\left(-\frac{(\alpha-\gamma x)^2}{2x}\right)$

where $\gamma > 0$, $\alpha > 0$, and the density is zero if $x \leq 0$.

Sources:

Metadata: ID: D95 | shortcut: wald | author: tomfaulkenberry | date: 2020-09-04, 12:00.