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Math Help - Determining the distribution of a random vector

  1. #1
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    Determining the distribution of a random vector

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

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

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

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

    Given a vector 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
    Last edited by phantom23; July 28th 2010 at 08:57 AM. Reason: clarification
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  2. #2
    frm
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    Hi,


    Quote Originally Posted by phantom23 View Post
    Given a vector 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 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 w_1, w_2, ... w_N and then try to fit it into an analytical PDF equation...

    HTH,
    Francesco
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