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Topic: fit power curve with best exponent to data
Replies: 4   Last Post: Feb 1, 2013 2:00 AM

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JK

Posts: 6
Registered: 12/9/12
Re: fit power curve with best exponent to data
Posted: Jan 30, 2013 2:51 PM
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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



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