Question

急!怎么用matlab求解Logistic模型中的三个参数？

将Logistic模型的方程变为y=b/(1+a*exp(-kt)),已知t=[0,5,10,24,33,48,57,72,96,120,144,168,192,216];y=[0,0.028,0.103,0.336,0.450,0.597,0.716,0.778,0.835,0.849,0.816,0.839,0.811,0.816].怎么求出参数a,b,k的值，要具体的程序，谢谢各位了！

Answer 1

建立m函数文件存为logistic1
function f=logistic1(b)
t=[0,5,10,24,33,48,57,72,96,120,144,168,192,216];y=[0,0.028,0.103,0.336,0.450,0.597,0.716,0.778,0.835,0.849,0.816,0.839,0.811,0.816];
f = y-b(1)./(1+b(2).*exp(-b(3).*t));

b0=[10,2,2];
>> b=leastsq('logistic1',b0)
b =

0.8221 13.9173 0.0818

或者cftool
General model:
f(x) = b/(1+a*exp(-k*x))
Coefficients (with 95% confidence bounds):
a = 13.92 (6.301, 21.53)
b = 0.822 (0.7911, 0.853)
k = 0.08184 (0.06479, 0.0989)

Goodness of fit:
SSE: 0.01404
R-square: 0.9898
Adjusted R-square: 0.9879
RMSE: 0.03572