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Subject: Re: fit power curve with best exponent to data
Date: Wed, 30 Jan 2013 19:51:08 +0000 (UTC)
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"Tom Lane" <tlane@mathworks.com> wrote in message <kebk50$bq1$1@newscl01ah.mathworks.com>...
> >> I'm attempting to fit the following equation to a set of data 
> >> characterizing something's autocorrelation function:
> >>
> >> y=e^(a*x)^n
> 
> Your y seems to drop off exponentially, so you want the exponent to be 
> negative, and you're raising it to a power that may not be an integer. If I 
> change your function I can do the following to fit it:
> 
> >> myexp = fittype('exp(a*(abs(x-b)^n))')
> myexp =
>      General model:
>      myexp(a,b,n,x) = exp(a*(abs(x-b)^n))
> >> fit(x,y,myexp,'start',[-20,4.47,1])
> ans =
>      General model:
>      ans(x) = exp(a*(abs(x-b)^n))
>      Coefficients (with 95% confidence bounds):
>        a =      -103.6  (-115.1, -92.15)
>        b =       4.475  (4.474, 4.475)
>        n =       1.065  (1.035, 1.094)
> 
> While you may not want this function, I hope this illustrates what you can 
> try with a function that you choose yourself.
> 
> -- Tom 

Hi Tom,

Yeah that's exactly what I was looking for, I'm just having trouble getting one type of model to work: an 'x-exponential' form where f(x) = exp[-(|z|/L)^x]. But thanks for the pointer towards 'fit'.

Jack