Determination of the Uncertainties in S-Curve Logistic Fits
Preprint
- 4 January 2022
- preprint
- Published by Center for Open Science in OSF Preprints
Abstract
Look-up tables and graphs are provided for determining the uncertainties during logistic fits, on the three parameters M, α and to describing an S-curve of the form: S(t) = M/(1+exp(-α(t-t0))).The uncertainties and the associated confidence levels are given as a function of the uncertainty on the data points and the length of the historical period. Correlations between these variables are also examined; they make “what-if” games possible even before doing the fit.The study is based on some 35,000 S-curve fits on simulated data covering a variety of conditions and carried out via a χ2 minimization technique. A rule-of-thumb general result is that given at least half of the S-curve range and a precision of better than 10% on each historical point, the uncertainty on M will be less than 20% with a 90% confidence level.Keywords
All Related Versions
- Published version: Technological Forecasting and Social Change, 46 (2), 153.
This publication has 0 references indexed in Scilit: