Proof: Probability density function of the von Mises distribution
Index:
The Book of Statistical Proofs ▷
Probability Distributions ▷
Univariate continuous distributions ▷
von Mises distribution ▷
Probability density function
Metadata: ID: P534 | shortcut: vm-pdf | author: JoramSoch | date: 2026-04-21, 15:08.
Theorem: Let $X$ be a random variable following a von Mises distribution:
\[\label{eq:vm} X \sim \mathrm{vM}(\mu, \kappa) \; .\]Then, the probability density function of $X$ is
\[\label{eq:norm-pdf} f_X(x) = \frac{1}{2 \pi I_0(\kappa)} \cdot \exp \left[ \kappa \cos(x-\mu) \right] \; .\]Proof: This follows directly from the definition of the von Mises distribution.
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Sources: Metadata: ID: P534 | shortcut: vm-pdf | author: JoramSoch | date: 2026-04-21, 15:08.