I am looking for some candidate functions to model some data that is somewhat bell shaped, but more flat at the top - something like this:
I was previously using two sigmoid functions, flipping one, and joining them in the middle, but this presents some mechanistic problems so I'd rather use just one function. A simple parabola doesn't work, neither does a normal curve - it needs to be somewhat flat on top.
I think dose-response curves tend to work well but I have had trouble finding the equations for ones that are symmetric about a central axis (go up then down).
I'm going to take a few candidate functions and find which is the best fit to my data using AICc in R.
