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Re: How to implement a summation function for numerical solving?

From: andrewcd
Subject: Re: How to implement a summation function for numerical solving?
Date: Thu, 16 Jun 2011 06:49:37 -0700 (PDT)

Thanks again Liam.  

I am running Octave 3.2.3 in Ubuntu (Linux), on a 64-bit lenovo thinkpad
x201.  When QtOctave starts, it tells me: 

GNU Octave, version 3.2.3
Copyright (C) 2009 John W. Eaton and others.
This is free software; see the source code for copying conditions.
FITNESS FOR A PARTICULAR PURPOSE.  For details, type `warranty'.

Octave was configured for "x86_64-pc-linux-gnu".

What do you mean by tolerances?  Is this the degree of change that is needed
between each iteration before the equation is considered "solved"?  How does
one change these?  And is it a change to fsolve or to some other command?

I am pretty sure (but not perfectly sure) that the equation should only have
one solution.  Basically what the code is doing is taking statistical moment
constraints and fitting the least-biased distribution that satisfies those
constraints.  Once I solve my current problem I want to add in higher
moments like skewness and kurtosis.  

In fact, once I add in skewness (f3 = ((x - mu).^3)./(variance.^1.5);), and
I manually iterate by taking the results and plugging them into the guesses,
I can often eventually end up at a stable, if wrong, solution.  The EV is a
sort of hacked numerical integral from -inf to .5 -- it should match the
mean if my code is working properly.  Not only does EV consistently not
match the mean, but skewness is backwards, and the solutions take several
manual iterations to become stable.

I think that I have both code problems (Octave not iterating enough) as well
as some fundamental problems (my approach to implementing MaxEnt has some
flaw in it).  

Any thoughts on how I can solve the former?  Thoughts on the later would be
a welcome bonus.

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