Proof: Probability density function of the Wald distribution
Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate continuous distributions ▷ Wald distribution ▷ Probability density function
Metadata: ID: P162 | shortcut: wald-pdf | author: tomfaulkenberry | date: 2020-09-04, 12:00.
Theorem: Let $X$ be a positive random variable following a Wald distribution:
\[\label{eq:wald} X \sim \mathrm{Wald}(\gamma, \alpha) \; .\]Then, the probability density function of $X$ is
\[\label{eq:wald-pdf} f_X(x) = \frac{\alpha}{\sqrt{2\pi x^3}}\exp\left(-\frac{(\alpha-\gamma x)^2}{2x}\right) \; .\]Proof: This follows directly from the definition of the Wald distribution.
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Sources: Metadata: ID: P162 | shortcut: wald-pdf | author: tomfaulkenberry | date: 2020-09-04, 12:00.