How to find (using R) the function which my experimental data follow?

I have an experimental time-depending data (Mean as a function of Time). I want to find the function which my data follow. I have already tried fitdistr and Gam, but it hasn't really helped. Could anyone help me to find out the way to get any meaningful solution?

Here are the examples of the experimental data growth curves. For the 1st one I have assumed that it follows the Gompertzt function.

Thank you in advance!

• Based on your knowledge of the subject matter, is there a particular functional form of how mean values change with time that you expect? For example, for the first example you suggest a Gompertz function (not to be confused with a Gompertz distribution). Do you have a similar functional form in mind for the second case, based on your understanding of the subject matter?
– EdM
Jul 14, 2015 at 13:59

1 Answer

If by the "Gompertzt" function (is the final "t" deliberate?) you mean this, but with an offset:

$y(t)=d+ae^{-be^{-ct}}$

then it cannot fit your data, since the trend in the data at higher $t$ doesn't asymptote to a fixed value (as the Gompertz does), but comes back down:

Your second curve looks something like a slightly smoothed exponential (or perhaps something slightly heavier tailed than exponential), with a small bump; there are various possibilities for describing it (and depending on what you want, perhaps the bump as well) -- but in both cases, if at all possible, theory should inform the choice of functions.