1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Curve fitting of summed normal distributions

  1. Jun 4, 2012 #1

    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:

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

    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:

    X = (x_1,x_2,...,x_n)


    \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.

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Curve fitting of summed normal distributions
  1. Normal Distributions (Replies: 4)

  2. Fitting A Curve (Replies: 1)

  3. Curve fitting (Replies: 0)