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From: "OR Stats" <stats112@gmail.com>
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Subject: Coding Probability Density (that is a large summation)
Date: Fri, 9 May 2008 11:34:03 +0000 (UTC)
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Hello M-Community:

I am fitting a density to my data.  I would therefore like
to estimate parameters of the density function based on my
data.  The density, however, is expressed as a summation. 
It is not one of the preconfigured densities found in MATLAB.  

The summation has 100 terms and cannot be re-expressed in
simpler form.  And rather than literally writing every term,
it would be easier to write a loop.  But how may I code this
estimation as such in MATLAB?

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?

Thanks in advance for your thoughts and suggestions.