I'm working on a method to predict certain things to change, for this i need to create a function with the following parameters:
- av: Average; >= 0
- max: Maximum value; < av; can be much larger than av
- v - Value; > 0; < max
The function needs to end up between 0 and 1 and i want to calculate a smooth curve with most increase around av. My first approach has been to first solve both problems independently, however getting both combined is where i fail as linear interpolation of course doesn't work and f(v) must be always greater than previous numbers as the v raises.
What i currently have:
$\left(\frac{v}{av}\right)^{2}$
$1-\left(\frac{max-v}{max-av}\right)^{2}$