Timeline for Fitting an exponential mixture model with interval constraints on the mixture weights

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May 22, 2012 at 14:24	comment	added	whuber♦		I found a good five-parameter fit as a rational function of $\exp(x)$ and $\exp(2 x)$. It suggests the second and third data points (from the left) are outliers (there's a hint of that in your last plot) and it slightly overestimates values for larger $x$. A case could be made for finding one fit for the most negative values of $y$ (less than $-300$, say) and another for the rest, but its merit depends on the scientific purposes of the fitting exercise, of which we unfortunately still remain ignorant.
May 21, 2012 at 22:17	comment	added	Emre		@whuber: Thanks for the software suggestion. I got the double exponential to fit all right (you can see it in the plot), but the fit was not good enough in my opinion so I sought a better model. Did you find a better fit with the mixture model?
May 21, 2012 at 22:10	comment	added	whuber♦		Nice--but you are working too hard. See new.nutonian.com/download. Use it to explore reasonable fits, then analyze them in greater detail with Mathematica. Incidentally, Mathematica can converge to a modest fit with the double-exponential formula: you need to supply better starting values, that's all.
May 21, 2012 at 22:02	history	edited	Emre	CC BY-SA 3.0	added 412 characters in body
May 21, 2012 at 21:50	history	answered	Emre	CC BY-SA 3.0