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I'm trying to fit a function that describes the following data, ideally with as few parameters as possible: Asymmetric S-shape growth curve. The data has the following properties:

  • X and Y go from 0 to 1
  • It is an S-Shape growth function.
  • The inflection point is not necessarily at X or Y = 0.5
  • Growth is initially slow, but then becomes more rapid. The opposite of the Gompertz growth curve to my understanding.

If it helps, here is the data from the graph:

X = [0 0.1818 0.3636 0.5455 0.7273 0.8182 0.9091 1.0000]

Y = [0 0.01 0.025 0.15 0.4 0.8 0.98 1]

yrom1
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1 Answers1

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I think using a function from the sigmoid family might be a good start. The Gompertz growth curve is part of this family:

$$f(x) = \frac{a}{b + e^{-kx}} + c$$

Where $a$, $b$, $c$, and $k$ are the model parameters.

If this curve is too symmetrical you can try a more generic sigmoid-esque curve:

$$f(x) = \frac{1}{1 + ae^{-k_1 x} + be^{-k_2 x}} + c$$

Hope this helps.

corner3
  • 400