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Curve fitting of summed normal distributions

  1. Jun 4, 2012 #1
    Hi,

    I have a dataset of a random variable whose probability density function can be fitted/modelled as a sum of N probability density functions of normal distributions:

    [itex]
    F_X(x) = p(\mu_1,\sigma_1^2)+p(\mu_2,\sigma_2^2)+\ldots+p({\mu}_x,\sigma_x^2)
    [/itex]

    I am interested in a fitting method can robustly determine the values of [itex]\mu_1,\sigma_1,\mu_2,\sigma_2,[/itex] etc

    Note this is NOT convolution of normal distributions.
     
    Last edited: Jun 4, 2012
  2. jcsd
  3. Jun 5, 2012 #2
    These folks have put a lot of time and thought into your problem

    http://www.sigmaplot.com/products/peakfit/peakfit.php [Broken]

    and they have free 30 day trial evaluations.
     
    Last edited by a moderator: May 6, 2017
  4. Jun 5, 2012 #3
    Interesting, any idea what method they use? Expectation-Maximization?
     
  5. Jun 5, 2012 #4
    Edit: I guess in particular, this is the equation I'm trying to maximize, given an input vector:


    [itex]
    X = (x_1,x_2,...,x_n)
    [/itex]

    Maximize:

    [tex]
    \begin{equation}
    \prod_{j=1}^n\sum_{i=1}^k \frac{p_i}{\sqrt{2\pi} \sigma_i} \exp(-\frac{(x_j-\mu_i)^2}{2\sigma_i^2})

    Edit: I found a nice paper tackling this exact problem using EM.
    \end{equation}
    [/tex]

    Subject to [tex] \sum_{i=1}^{k} p_i = 1 [/tex]

    When I say maximize, I mean to find the model parameters [tex] \mu_i, \sigma_i, p_i [/tex]
     
    Last edited: Jun 5, 2012
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