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.
∎
Sources: Metadata: ID: P162 | shortcut: wald-pdf | author: tomfaulkenberry | date: 2020-09-04, 12:00.