Definition: Circular random variable
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Probability theory ▷
Random variables ▷
Circular random variable
Sources:
Metadata: ID: D229 | shortcut: rvar-circ | author: JoramSoch | date: 2026-04-20, 15:18.
Definition: Let $X$ be a random variable with possible outcomes $\mathcal{X}$. Then, $X$ is called a circular random variable, if $\mathcal{X} = [0, 2 \pi)$ and if the probability density function of $X$ satisfies
\[\label{eq:pdf-circ} f_X(x + 2 \pi k) = f_X(x) \quad \text{for all} \quad k \in \mathbb{Z} \; .\]- Wikipedia (2026): "Circular distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2026-04-20; URL: https://en.wikipedia.org/wiki/Circular_distribution#Examples.
Metadata: ID: D229 | shortcut: rvar-circ | author: JoramSoch | date: 2026-04-20, 15:18.