Question

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)),t=[0,1,2,3,4,5,6,7,8,9,10,11,12,13],y=[2399.14,2269.8,2577.467,2804.28,2552.35,2562.24,2488.96,2914.00,2740.54,2690.78,2754.27,2837.92,2971.55,3025.11]怎么求出参数a,b,k的值,要具体的程序.

Answer 1

这是个拟合问题，可这样：
x=[0,1,2,3,4,5,6,7,8,9,10,11,12,13];
y=[2399.14,2269.8,2577.467,2804.28,2552.35,2562.24,2488.96,2914.00,2740.54,2690.78,2754.27,2837.92,2971.55,3025.11];
f=fittype('b/(1+a*exp(-k*x))');
[fity,g]=fit(x',y',f)
结果是：
fity =

General model:
fity(x) = b/(1+a*exp(-k*x))
Coefficients (with 95% confidence bounds):
a = -0.9972
b = 6.817
k = 18.01

g =

sse: 9.5318e+07
rsquare: -149.6950
dfe: 11
adjrsquare: -177.0941
rmse: 2.9437e+03