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Hello:

I need to fit some data to the following implicit equation:

((1-y)^(1-b)/y)=exp(-kt)

t is a vector containing time values and y is a vector containing current values. for each series of data y vs t, I need to determine b and k

b has to be between 0 and 1, and k needs to be greater than 0.

I have both the optimization and the curve fitting toolboxes.

Any suggestions on what tools to use (lsqcurvefit? something else? would be very appreciated)

Thanks!

Jeff Miller
on 14 Jan 2021

Edited: Jeff Miller
on 14 Jan 2021

I would suggest using fminsearch. The error function to be minimized would be something like:

function thiserr = err(x,y,t)

b = x(1);

k = x(2);

thiserr = sum( (((1-y).^(1-b)./y) - exp(-kt))^2 );

end

You should be able to find examples of how to use fminsearch if you need more detail on how to call it. In your case y and t are "extra parameters". Look here for information on how to handle that.

John D'Errico
on 16 Jan 2021

My thought would be the lazy solution. If your model is:

((1-y)^(1-b)/y)=exp(-kt)

then log the model. That is, we know that

(1-b)*log(1-y) + k*t = log(y)

With one more step, this reduces to

-b*log(1-y) + k*t = log(y) - log(1-y)

You can compute the parameters k and b using a simple linear regression now. Thus, if y and t are column vectors, we have:

bk = [-log(1-y),t] \ (log(y) - log(1-y));

so bk is a vector of length 2, contining the estimates for b and k respectively. If you find that b or k are estimated to be something outside of the valid region, then I would first consider if this is a reasonable model, but then you could just use lsqlin to estimate them, since lsqlin does provide bound constraints.

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