Logistic曲线的三种参数估计方法及matlab算法实现

clear;clc; %Nair算法 %author:朱伟杰 %date:2018-1-24 X=[480.9,522,468.8,469.5,573.8,737.8,869.8,933.7,977.2,... 997.7,1120.3,1176.1,1284.8,1422.1,1462.1,1499.7,... 1473.1,1539.2,1637,1771,1886.5,1994.6,2145.7,2292,... 2396.8,2387,2484.4,2580.8,2750.2,2915.7,3163.8,3231.9,... 3319.5,3319.6,3484.,3550.6,3613.9,3833.1,4471.2,5283,... 5803.2,6415.5,6797.9,7033.5,7636.3,8209.8,8979.1] n=length(X)-1 for t=1:n Z(t)=1/X(t)-1/X(t+1) S(t)=1/X(t)+1/X(t+1) end X1=[ones(46,1) S(1:n)'] Y=Z' [B,Bint,r,rint,stats]=regress(Y,X1)%最小二乘（OLS） gamma=B(1,1) beta=B(2,1) b=log((1-beta)/(1+beta)) c=gamma*(1+exp(b))/(2*(exp(b)-1)) a=exp((sum(log(1./X(1:n)-c))-n*(n+1)*b/2)/n) XX=1965:2016 YY=1./(c+a*exp(b*([XX-1965]))) plot(XX,YY,'r-o') hold on plot(XX(1:length(X)),X,'g-^') legend('预测值','实际值') xlabel('年份');ylabel('二氧化碳排放量'); title('二氧化碳预测值和实际值曲线图(Nair法)') set(gca,'XTick',[1965:2:2017]) grid on format short; forecast=YY(end-4:end)%CO2排放量的预测结果 MAPE=sum(abs(YY(1:n+1)-X)./X)/length(X)%平均相对差值 a,b,c