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Double exponential decay curve

 
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emub24



Joined: 14 Mar 2018
Posts: 1

PostPosted: Wed Mar 14, 2018 10:04 am    Post subject: Double exponential decay curve Reply with quote

I'd like to fit a curve to the double exponential decay equation

which is y = a*exp(-bx)+c*exp(-dx).

I think I need to add optimizations for my data as I'm getting a flat line for each curve.

Can any one explain how to define the functions in the application and which part is the constant, rate and amounts. I'm finding it difficult to find a clear explanation on double exponential decay curves online.

All the best

confused
Confused
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David
Site Admin


Joined: 25 Nov 2006
Posts: 1960
Location: Chapel Hill, NC

PostPosted: Sat Mar 24, 2018 11:24 am    Post subject: Reply with quote

The issue might be that the range is too large for the standard least squares fit. In DataGraph, this is fixed by allowing you to fit it logarithmically, but in DataTank this option is not available.

Here is one way to explain it. If the data is approximately 0.1*exp(-x) + 10*exp(-5x) on for example [0,6] the values are very small on the portion where x>2. So if f(x) = a*exp(-bx)+c*exp(-dx), instead of minimizing the distance f(x)-y(x) you minimize log(f(x))-log(y(x)) = log(f(x)/y(x)). That is esstentially minimizing the relative error instead of the absolute error.

If this is a DataGraph question, that should fix it. If this is a DataTank question the workaround is to map the data using log and then add log to the fit function.

David
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