Distribution of a projected multivariate t variable

by WarrenBuffet   Last Updated November 17, 2017 13:19 PM

Say $\boldsymbol x \sim t_5(\boldsymbol\mu, \boldsymbol\Sigma)$ is a $p$-dimensional multivariate t distributed random variable with $\boldsymbol \mu \in \mathbb{R}^p$ and $\boldsymbol \Sigma \in \mathbb{R}^{p\times p}$. Be $\boldsymbol w \in \mathbb{R}^p$ a constant vector.

What are the probability density and distribution of $\boldsymbol w^T \boldsymbol x \in \mathbb{R}$? Are there an analytical expression for the pdf / cdf?

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