Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Wald distribution ▷ Probability density function

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.