Relate › Nonlinear / curve fitting

Gompertz growth

Gompertz growth fits y = A · exp(−B · exp(−C · x)), an asymmetric sigmoid alternative to logistic growth.

What is Gompertz growth?

Asymmetric S-curve — the inflection point sits at A/e ≈ 0.37·A (not at A/2 like the logistic). Used historically for tumour growth, bacterial colony growth, mortality rates with age (Gompertz law).

Compared to logistic_growth: Gompertz has a slower-than-symmetric approach to the upper asymptote; logistic is symmetric around its inflection point. Both have 3 parameters; pick by AIC if you're unsure.

When should I use Gompertz growth?

  • Tumour growth.
  • Microbial growth.
  • Any growth curve with asymmetric approach to the asymptote.

What data does it need?

Numeric time X + Y.

What does it report?

A (asymptote) + B (offset) + C (rate) with CIs.

How do I interpret the result?

Gompertz vs logistic visually similar — use AICc to discriminate when both converge.

See also

References

  • Gompertz (1825). On the nature of the function expressive of the law of human mortality. Philos. Trans. R. Soc. 115.