# Determining the distribution of a random vector

#### phantom23

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 (Clapping)

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#### frm

Hi,

Given a vector $$\displaystyle w$$, how do I determine which distribution fits it best?
I think that given a _single_ vector w you cannot determine any distribution.
If instead you have multiple measurements for each component $$\displaystyle w_i$$ of the vector w (with i=1...N), then I think you can build a (N+1)-dimensional histogram (Histogram - Wikipedia, the free encyclopedia) i.e. a graph of frequency vs the variables $$\displaystyle w_1, w_2, ... w_N$$ and then try to fit it into an analytical PDF equation...

HTH,
Francesco