Hierarchical Gompertz model

Ok just to check my thinking here before I model this:
Given my gompertz function, where t = time in days:

\\Y = f(t) = Ae^{-exp(-k( t - d ))}

I said let:

\\y_{max} = Ae^{-exp(-k( t_{max} - d ))}

Applied some algebra and got:

\\f(t) = y_{max} \cdot e^{(exp(-k(t_{max} - d) - exp(-k(t - d) ))}

where y_max, t and t_max are all taken from data meaning I now have a 2 parameter model.

Am I in thinking along the right lines here? Presumably then after I would fit this I then calculate A in the generated data section using the middle equation here ?

@mevers - I hope you don’t mind me part-invading your thread!

Edit: test for single country fits - i.e. no hierarchy look good so far! Will update as I progress!
Edit2: Algebra incorrect deriving last equation - fixed now.