Hello everyone. I have a rather unusual question and thank you very much in advance.
For an economics paper I am trying to create a function f(x) with four additional parameters:
The function should fulfill following aspects:
f(x) 0.
.
f(x) has a local extrema at , i.e.
with
between and and between and there should be monotone growth(positive or negative).
Every possible non negative combination of should be achievable.(If adding a size constraint or a constraint on the maximum difference between helps, thats ok as well.
There need not be a analytical solution, numerical would be quit satisfactory.
So far I have been experimenting with something like:
and .
Due to my economics back ground I also tried to take inspiration from the Nelson Siegel formula:
but without much success.
My problem is, that I can't seperate the position of the extreme from the value of , so I can not move a extrema horizontally.
If anyone has any idea, as two what constructions could be used, I would be very grateful.
Thanks a lot and have a nice day