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From Italo Maia <italom...@hotmail.com>
Subject RE: [math]
Date Fri, 06 Jul 2012 21:39:30 GMT

Hummm, so my assumption that my previous values for a, b and c were the best are wrong. I
calculated the resid and it is really smaller. Real thanks for that!
Any tips on calculating the r-squared?

Date: Fri, 6 Jul 2012 22:05:26 +0200
From: gilles@harfang.homelinux.org
To: user@commons.apache.org
Subject: Re: [math]

Hi.
 
If you are using the function
 
  a * Math.pow(t, b) * Math.exp(-c * t)
 
the gradient is:
 
  { Math.pow(t, b) * Math.exp(-c * t),
    a * Math.log(t) * Math.pow(t, b) * Math.exp(-c * t),
    -a * t  Math.pow(t, b) * Math.exp(-c * t) }
 
> // No idea what goes here. Nothing seems to work.
 
Well, the gradient (partial derivatives w.r.t the parameters) is the thing
that will work; the attached figure shows the data and the function that
fits it with
 a = 1.097378664278161
 b = 0.4273818336149512
 c = 0.01457006142420487
 
> 
> a, b and c for this example should be: A: 1.0782   B: 0.4583   C: 0.0166
 
The fit is slightly better with the values found by "CurveFitter"
(the "LevenbergMarquardt" algorithm actually).
 
Regards,
Gilles
 

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