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?

Finding distribution of distance from origin

https://stats.stackexchange.com/questions/25358/what-is-the-distribution-of-the-euclidean-distance-between-two-random-points-in