Index: The Book of Statistical ProofsProbability DistributionsUnivariate continuous distributionsWald 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 $x \leq 0$.

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