Set three random variables
\begin{equation*} X_1, X_2, X_3 \sim \mathcal{N}(\mu, \sigma) \end{equation*}
and their respective transformations
\begin{equation*} Y_1 = |X_1| \;,\; Y_2=|X_2| \;,\; Y_3= |X_3|. \end{equation*}
I know the densities for each $Y$s but I would like to find the distribution of
\begin{equation*} Z=Y_1+Y_2+Y_3. \end{equation*}
I saw an answer for two folded normals and I wasn't sure how to transpose it to my problem.
