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    $\begingroup$ Perfect as far as what I was hoping for. It is amazing how well the data matches the curve. Thank you! $\endgroup$ Commented Sep 16, 2013 at 21:31
  • $\begingroup$ @whuber You wrote $a>0$ and $s>0$, does the R code that you wrote respect these constraints? $\endgroup$ Commented Oct 8, 2014 at 8:36
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    $\begingroup$ @uvts That's a good question. $s\gt 0$ is not a constraint because the model for $-s$ is the same as that for $s$: this is just a way of assuring identifiability of $s$. Rather than constrain $a$ to be non-negative (which could be done) I find it both more informative and more general to allow the optimizer to fit the best unconstrained value of $a$ it can. $\endgroup$ Commented Oct 8, 2014 at 14:31