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From: Peter Perkins <Peter.PerkinsRemoveThis@mathworks.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Coding Probability Density (that is a large summation)
Date: Fri, 09 May 2008 16:51:48 -0400
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OR Stats wrote:

> It can be thought of as an optimization problem for which
> the parameters need to be recovered when the x's are
> observed.  E.g.,  density function f with unknown parameter a:
> 
> f(x) =  Sum _k=0 to 100_    { f1(a,k)*f2(x,a,k)}
> 
> Both f1 and f2 can be expressed analytically.  But clearly
> it is unfortunate that f(x) is an infinite summation of the
> two functions multiplied together.  Since I am interested in
> is using my observed 'x''s to estimate 'a'.  How can I do
> this estimation in MATLAB?

In theory, this is no different than any other maximum likelihood problem, and 
could be solved using, for example, FMINSEARCH, FMINCON, MLE (in the Statistics 
Toolbox), or others.  In practice, who knows what statistical and numeric 
properties this likelihood function has.

Hope this helps.