Re: Curve fitting

• To: mathgroup at smc.vnet.net
• Subject: [mg29388] Re: Curve fitting
• From: "David M. Wood" <dmwood at slate.Mines.EDU>
• Date: Sat, 16 Jun 2001 02:47:59 -0400 (EDT)
• Organization: Colorado School of Mines
• References: <9gcmjl\$36g\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Mark Harder <harderm at ucs.orst.edu> wrote:
>     To get just the best-fit parameters plugged into your (nonlinear)
> function, you can use NonlinearFit. To get the parameters with statistics of
> the result, use NonlinearRegress.  Both are in the Statistics`NonlinearFit
> package.

> -----Original Message-----
> From: Tobin Fricke <tobin at splorg.org>
To: mathgroup at smc.vnet.net
> Subject: [mg29388]  Curve fitting
>>I'd like to find the parameters C1, C2, C3, C4, C5, such that the
>>expression "C1*Exp[x/C2] + C3*Exp[x/C4] + C5" best approximates a given
>>function (or, more directly, the distribution of a data series).  Any help
>>would be greatly appreciated.  (This is like the Poisson distribution, but
>>for two random variables, plus a constant offset... I think.)

Two remarks:

1. I have noticed in some cases that (at least for linear fits),
LinearRegression is far more numerically stable than Fit.  Maybe same
holds for NonLinear Fit?

2. IIRC, this functional form --sums of exponentials-- is notoriously
difficult to reliably fit.  I remember trying to fit some temperature
annealing data, and this issue came up.  I *think* I tried to fit the
high T range reliably (hoping one exponential dominated), then, using
the parameters I found, fit the low T.

For small x your fitting form looks like (c1 + c3 +c5) + (c1/c2 + c3/c4)x...
so there may be a whole locus of parameter values that fit reasonably
well.

--
David M. Wood
Department of Physics, Colorado School of Mines, Golden, CO 80401
Phone: (303) 273-3853; Fax: (303) 273-3840
e-mail: dmwood at physics.Mines.EDU ; NeXTMail welcome

```

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