DETERMINATION OF THE UNCERTAINTIES IN S-CURVE LOGISTIC FITS

Look-up tables and graphs are provided for determining the uncertainti es during logistic fits, on the three parameters M, alpha and t(o) des cribing an S-curve of the form: S(t) = M/1 + e(-alpha(t-t(o))). The un certainties and the associated confidence levels are given as a functi on of the uncertainty on the data points and the length of the histori cal period. Correlations between these variables are also examined; th ey make ''what-if'' games possible even before doing the fit. The stud y is based on some 35,000 S-curve fits on simulated data covering a va riety of conditions and carried out via a chi2 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 hitorical point , the uncertainty on M will be less than 20% with 90% confidence level .