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