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Determination of the Uncertainties in S-Curve Logistic Fits

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  • MODIS, THEODORE

    (CERN)

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.

Suggested Citation

  • Modis, Theodore, 1994. "Determination of the Uncertainties in S-Curve Logistic Fits," OSF Preprints n53pd_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:n53pd_v1
    DOI: 10.31219/osf.io/n53pd_v1
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    Cited by:

    1. Serrecchia, Michela, 2024. "Analysis of Internet development and internal digital divide by using the “.it” domain names as an indicator: Evidence from Italy," Telecommunications Policy, Elsevier, vol. 48(10).

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