This paper by Peter Pflaumer gives a bit more technical detail to the whole Gompertz/Gumbel lifespan thing. I need to remember that my model works, I just need a stable way of estimating the model parameters from which to start optimizing a fit. Pflaumer derives a formula for the mode, but it is still trancendental in the force scaling parameter.
Hmm, I should see what Garrett thinks of the economics of this distribution, since that's what it was originally developed for. He probably already knows all about it, why didn't I think to ask last weekend? Ah, because I started this on Sunday and saw him on Saturday :p.
I though this aught to do it for me, but it seems their rate has an extra
-ln(P) in it.
Desperate times call for going back to Gompertz' original paper.