David, your equations look good. My data is zeroed at fb-f, having subtracted the y-axis min of the points, so D(x1) = 0, makes it even simpler. As it seems that the fitted smooth spline model is of high quality (p<0.01), for my curent data, and I expect it should be so for most successful film tests, the R predict(x) function will safely give me the interpolated value of D(x), using the spline, for any point I need along the range of rel logE axis. So it looks like I'm now in position to use the curve to solve your equations for the CI condition, looking for the first occurrence of it, I suppose, from left, in case the condition could be fulfilled more than once on a strange curve. Thanks for the suggestion of optimize.fsolve in scipy, that's a great tip. I will try uniroot or rootSolve/multiroot in R. If I can't make it, I'll ask for your Python.
Last edited by Rafal Lukawiecki; 08-31-2013 at 06:12 AM. Click to view previous post history.