Logistic
An S-shaped rise from 0 to a plateau A. Use it for population growth, autocatalytic reactions and other growth that starts slowly, speeds up and then saturates.
Parameters
- Upper plateau. The lower plateau is 0.
- Growth rate, in inverse units of x. Larger values give a steeper step; negative values give a falling curve.
- Midpoint: the x at which y = A/2.
Tips
- curve.fit does not estimate starting values for this model, so enter guesses: A near the plateau, C near the midpoint, and B ≈ 4.4 divided by the distance in x over which y rises from 10% to 90% of A.
- The lower plateau is fixed at 0. For data that level off at another value, use a Custom Function such as
A/(1+exp(-B*(x-C)))+D. - For a step that is symmetric in log x, such as a dose–response curve, use Hill Sigmoid (4 Parameter).