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From: "OR Stats" <stats112@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Coding Probability Density (that is a large summation)
Date: Fri, 9 May 2008 22:41:04 +0000 (UTC)
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Thanks for your suggestion, Peter.  How would I express the
likelihood estimation in MATLAB when the density itself is
100 some terms?  Do I have an alternative to coding all 100
terms?  f1(a,k)*f2(x,a,k), where k is my index, which is
unrelated to my data points x themselves.

Peter Perkins <Peter.PerkinsRemoveThis@mathworks.com> wrote
in message <g02dh4$l7t$1@fred.mathworks.com>...
> 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.