I'm trying to solve the following least squares problem:

$\displaystyle \underset{x}{\text{min}} ||Ax - \tilde{b}||_2$

where $\displaystyle Ax = b$ and $\displaystyle \tilde{b} = b + w$

$\displaystyle w$ is a vector resulting from some operations and is not necessarily Gaussian. Also, I have access to $\displaystyle b$ and therefore, $\displaystyle w$. My question is as follows:

Given a vector $\displaystyle w$, how do I determine which distribution fits it best?

Thanks in advance! This is my first time here, and the presence of LaTeX is very heartening