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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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 Tom Lane Posts: 858 Registered: 12/7/04
Re: fit power curve with best exponent to data
Posted: Jan 30, 2013 12:09 PM

>> 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

Date Subject Author
1/30/13 JK
1/30/13 JK
1/30/13 Tom Lane
1/30/13 JK
2/1/13 Marc