What’s the distribution of $L_1$ norm of Gaussian random variables?

By | June 23, 2018

Suppose we have a Multivariate Gaussian random variable $X\sim N(\mu,\Sigma)$. What's the distribution of $\|X\|_1$?

My thinking: There are a lot of articles talking about the distribution of $\|X\|_2$, But how about $L_1$ norm?

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