The Gompertz function is a simple mathematical model for constrained growth as a function of time.
It was named after Benjamin Gompertz, who was a british mathematician and actuary.
It takes the form: \[ y(t)=a e^{-b e^{-c t}} \]
a, b, and c are the three parameters that describe the shape as the function varies with time, t
Gompertz Function
Modelling Constrained Growth
Brandon Bartell
Nerd
What is the Gompertz function?
Why use it?
- The Gompertz function is practical for its simplicity and power
- With 3 simple parameters, you can easily model
- Population growth with finite resources
- Tumor growth in a confined space
- Product/technology share uptake to peak share
What does each parameter do?
- Here are some examples showing how the curve moves with each parameter, leaving the other parameters fixed.
Playing with it yourself!
In order to understand what each parameter in the Gompertz function does, it is useful to play with each parameter and visually see it's effect on the shape of the curve.
My shiny app lets the user change the three parameters and the plotting range interactively.
Try it for yourself!