Determining the distribution of a random vector

Jul 2010
1
0
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)
 
Last edited:

frm

Mar 2010
6
0
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