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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: Sat, 10 May 2008 14:59:03 +0000 (UTC)
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I suppose the confusion is how to express the density when
symbolically it is 100+ terms...   

"OR Stats" <stats112@gmail.com> wrote in message
<g02ju0$46k$1@fred.mathworks.com>...
> Thanks for your suggestion, Peter.  How would I express the
> likelihood estimation in MATLAB when the density itself is
> 100 some terms?  Do I have an alternative to coding all 100
> terms?  f1(a,k)*f2(x,a,k), where k is my index, which is
> unrelated to my data points x themselves.
> 
> Peter Perkins <Peter.PerkinsRemoveThis@mathworks.com> wrote
> in message <g02dh4$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.
>