Index: The Book of Statistical Proofs ▷ Statistical Models ▷ Multivariate normal data ▷ Multivariate Gaussian ▷ Multivariate normally distributed data

Definition: Multivariate normally distributed data are defined as a set of $p$-dimensional vectors $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$ with $y_i \in \mathbb{R}^p, \; i = 1,\ldots,n$, independent and identically distributed according to a multivariate normal distribution with mean vector $\mu \in \mathbb{R}^p$ and covariance matrix $\Sigma \in \mathbb{R}^{p \times p}$

\[\label{eq:mvn} y_i \sim \mathcal{N}(\mu, \Sigma), \quad i = 1, \ldots, n\]

where $\mu$ is a $p$-dimensional real vector and $\Sigma$ is a $p \times p$ positive-definite matrix.

 
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Metadata: ID: D223 | shortcut: mvn-data | author: JoramSoch | date: 2025-06-20, 14:46.