Definition: Univariate von Mises
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The Book of Statistical Proofs ▷
Statistical Models ▷
Periodic data ▷
Univariate von Mises ▷
Definition
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Metadata: ID: D232 | shortcut: vm-data | author: JoramSoch | date: 2026-04-23, 15:45.
Definition: A univariate von Mises data set is given by a set of real numbers $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ with $y_i \in [0, 2 \pi), \; i = 1,\ldots,n$, independent and identically distributed according to a von Mises distribution with unknown circular mean $\mu \in [0, 2 \pi)$ and unknown reciprocal dispersion $\kappa > 0$:
\[\label{eq:vm} y_i \sim \mathrm{vM}(\mu, \kappa), \quad i = 1, \ldots, n\]- Bishop CM (2006): "Periodic variables"; in: Pattern Recognition for Machine Learning, sect. 2.3.8, p. 108; URL: http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf.
Metadata: ID: D232 | shortcut: vm-data | author: JoramSoch | date: 2026-04-23, 15:45.