MATLAB: How to solve this function below

solve function

parameters：a b c
KNOWN:(x1,y1),(x2,y2)… …(xn,yn) How can I figure out all the parameters by using MATLAB?

Best Answer

Your code was fine, but your variables were pretty badly scaled, so I think the fit was behaving badly numerically. Here is some code where I rescaled your time variable for the fit (and then rescaled it back to display):
TIME_SCALE = 1000;
time = [1992   1993   1994   1995   1996   1997   1998   1999   2000   2001   2002   2003   2004   2005   2006   2007   2008   2009   2010   2011   2012 ];
time = time/TIME_SCALE;
Y6711 = [0.001549451  0.001406211  0.001811241  0.001661079  0.002009743  0.001669221  0.002511118  0.001794201  0.003740947  0.00441657  0.004941945  0.004628348  0.004379816  0.005177686  0.004069535  0.004633793  0.007670759  0.009623098  0.009783128  0.010096395  0.012705525];
beta=nlinfit(time,Y6711,@curvefun,[0.5 0.5 0.5]);
a = beta(1);
b = beta(2);
c = beta(3);
%test the model
xx = min(time):(1/TIME_SCALE):max(time);
yy = a./(1+exp(b.*time+c));
plot(TIME_SCALE*time,Y6711,'o',TIME_SCALE*xx,yy,'r')
You are right that the initial guess is subjective. It is best to put in something that is approximately the right magnitude and sign if you can. For example, you know your parameter b has to be negative. But MATLAB figured it out here.
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