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Parameter estimation

  1. Jun 25, 2007 #1
    I have a probability distribution of the form [tex]\sum_{i=0}^n f(n,x,y)[/tex]. There is no closed form expression for it. I need to know if there is any method that I can use to estimate the parameters {n, x, y} given some data from the above distribution.
    I've tried a maximum likelihood approach, but I'm having trouble getting the derivative with respect to n. Is it possible to get this derivative, and use a maximum likelihood approch to estimate n
     
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  3. Jun 25, 2007 #2

    EnumaElish

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    Is your f indexed by i? If not, then you have (n+1)f(n,x,y), which is differentiable w/r/t/ n, as long as f is.

    If f is indexed by i, then you might think of the sum as an integral and may be able to apply Leibniz's Rule (see under "Alternate form": http://en.wikipedia.org/wiki/Leibniz's_rule).
     
    Last edited: Jun 25, 2007
  4. Jun 28, 2007 #3
    Thanks for the reply. I had a look at that Leibniz's Rule link, but I'm not fully sure how to go about using it??

    Anyway, I was thinking of a slightly more simple idea. I basically need an estimate of the 3 parameters {n, x, y}, preferiably using MLE. Since it's difficult to get the derivative w.r.t n, I was thinking of trying various values of n (say n=1,..,50), and for each value of n estimate MLE of x,y.

    So basically, I now end up with 50 different estimates for {n, x, y}. So my question is, is there any mathematical way to tell which one of these 50 estimates is the best one? ie. Is there some sort of likelihood test I could use?
     
  5. Jun 28, 2007 #4

    EnumaElish

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    I'd just look at the (log) likelihood numbers and select the largest.
     
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