Fitting a Second-Order Exponential Function in MATLAB

Question

I'm sitting with measurements of radiation intensity over time on two unstable isotopes (in the same sample). The radiation is of two different energies, leaving me with a second-order exponential formula for decay - similar to the formula for exponential decay but with two terms, these being identical but for the different starting intensities and the different half-lives of the different isotopes.

f(t)=(I_0,1)*e^(-lambda_1*t) + (I_0,2)*e^(-lambda_2*t) %(eventually with a constant term as well)

There are numerous ways to fit the data to this function, but how do I get the uncertainties
(for example in the form of standard deviation) for the fitted variables (the half-lives and initial intensities)?

Answer 1

Using the NONLINEARMODEL class, you can get the standard errors of the fitted variables as follows:

fitFunc = @(b,t) b(1)*exp(-b(2)*t) + b(3)*exp(-b(4)*t);

%# leave off the semicolon for nicely formatted output
mdl = fitnlm(tVector, energies, fitFunc, initialGuessForBeta)

%# SE of coefficients
mdl.Coefficients.SE