Which function can I use to fit my plot? Looks like a sigmoid function with a dip at the top

Question

I was wondering which function I could use to fit to the following plot:

Thanks for the help!

Answer 1

Something like this maybe? A slope with steepness controlled by $\alpha$, and subtract a bell curve centered at $d$ with width controlled by $\gamma$ and vertical scaling controlled by $\beta$: $$\frac{e^{-\alpha x}}{1-e^{\alpha x}}+1-\beta \left(e^{-\frac{(x-d)^2}{2 \gamma }}\right)$$

Other than that, if you want curve where you know precisely $a$,$b$,$c$,$d$,$e$,$f$ then I suggest breaking it into a piecewise curve.

Edit: The above is not so great near zero. This below is a bit simpler for curve fitting: $$ 1-e^{-\alpha(x-p)}-\beta e^{-\frac{(x-d)^2}{2 \gamma }} $$