1.3. Multivariate Normal Distribution
A probability distribution that plays a pivotal role in multivariate analysis is multivariate normal distribution. We say that y has a multivariate normal distribution (with a mean vector μ and the variance-covariance matrix Σ) if its density is given by
In notation, we state this fact as y ~ Np(μ, Σ). Observe that the above density is a straightforward extension of the univariate normal density to which it will reduce when p = 1.
Important properties of the multivariate normal distribution include some of the following:
Let Ar × p be a fixed matrix, then Ay ~ Nr (Aμ, AΣA′) (r ≤ p). It may be added that ...
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