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Determination of the Uncertainties in S-Curve Logistic Fits

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  • MODIS, THEODORE

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 90% confidence level.

Suggested Citation

  • Modis, Theodore, 1994. "Determination of the Uncertainties in S-Curve Logistic Fits," OSF Preprints n53pd, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:n53pd
    DOI: 10.31219/osf.io/n53pd
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    Cited by:

    1. Debecker, Alain & Modis, Theodore, 2021. "Poorly known aspects of flattening the curve of COVID-19," Technological Forecasting and Social Change, Elsevier, vol. 163(C).
    2. Michalakelis, C. & Sphicopoulos, T., 2012. "A population dependent diffusion model with a stochastic extension," International Journal of Forecasting, Elsevier, vol. 28(3), pages 587-606.
    3. Jonathan Beck, 2007. "The sales effect of word of mouth: a model for creative goods and estimates for novels," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 31(1), pages 5-23, March.
    4. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    5. Miranda, L.C.M. & Devezas, Tessaleno, 2022. "On the global time evolution of the Covid-19 pandemic: Logistic modeling," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    6. Modis, Theodore, 2019. "Forecasting energy needs with logistics," Technological Forecasting and Social Change, Elsevier, vol. 139(C), pages 135-143.
    7. Modis, Theodore, 2013. "Long-Term GDP Forecasts and the Prospects for Growth," OSF Preprints aqcht, Center for Open Science.
    8. Anton Badev & Stanimir Kabaivanov & Petar Kopanov & Vasil Zhelinski & Boyan Zlatanov, 2024. "Long-Run Equilibrium in the Market of Mobile Services in the USA," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
    9. Charlie Wilson:, 2010. "Growth dynamics of energy technologies: using historical patterns to validate low carbon scenarios," GRI Working Papers 32, Grantham Research Institute on Climate Change and the Environment.
    10. Miriam Steurer & Robert J. Hill & Markus Zahrnhofer & Christian Hartmann, 2012. "Modelling the Emergence of New Technologies using S-Curve Diffusion Models," Graz Economics Papers 2012-05, University of Graz, Department of Economics.
    11. Wilson, Charlie, 2010. "Growth dynamics of energy technologies: using historical patterns to validate low carbon scenarios," LSE Research Online Documents on Economics 37602, London School of Economics and Political Science, LSE Library.
    12. Bento, Nuno & Fontes, Margarida, 2016. "The capacity for adopting energy innovations in Portugal: Historical evidence and perspectives for the future," Technological Forecasting and Social Change, Elsevier, vol. 113(PB), pages 308-318.
    13. S. Mahmuda & T. Sigler & E. Knight & J. Corcoran, 2020. "Sectoral evolution and shifting service delivery models in the sharing economy," Business Research, Springer;German Academic Association for Business Research, vol. 13(2), pages 663-684, July.

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