Definition: Wald distribution
Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate continuous distributions ▷ Wald distribution ▷ Definition
Sources:
Metadata: ID: D95 | shortcut: wald | author: tomfaulkenberry | date: 2020-09-04, 12:00.
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 $x \leq 0$.
- Anders, R., Alario, F.-X., and van Maanen, L. (2016): "The Shifted Wald Distribution for Response Time Data Analysis"; in: Psychological Methods, vol. 21, no. 3, pp. 309-327; URL: https://dx.doi.org/10.1037/met0000066; DOI: 10.1037/met0000066.
Metadata: ID: D95 | shortcut: wald | author: tomfaulkenberry | date: 2020-09-04, 12:00.