a.m

基于极大嫡谱估计准则对变形数据进行预测 基于MATLAB平台编制了相应程序

Fx=Exp[a]+Exp[a]*b*x+Exp[a]*(c+1/2*b^2)*x^2+Exp[a]*(d+b*c+1/6*b^3)*x^3+Exp[a]*(e+b*d+1/2*c^2+1/2*c*b^2+1/24*b^4)*x^4

Fx=exp[a+b*x+c*x^2+d*x^3+e*x^4]
FX=Series[Fx,{x,0,5}]
Fx=Normal[%]

clear
k1=20.271;
k2=415.11;
k3=8566.1;
k4=177840;
Fx=Exp[a]+Exp[a]*b*x+Exp[a]*(c+1/2*b^2)*x^2+Exp[a]*(d+b*c+1/6*b^3)*x^3+Exp[a]*(e+b*d+1/2*c^2+1/2*c*b^2+1/24*b^4)*x^4
m0=Integrate[Fx,{x,0,1000}]
m1=Integrate[Fx*x,{x,0,1000}]
m2=Integrate[Fx*x^2,{x,0,1000}]
m3=Integrate[Fx*x^3,{x,0,1000}]
m4=Integrate[Fx*x^4,{x,0,1000}]
p0=m0==1
p1=m1==k1
p2=m2==k2
p3=m3==k3
p4=m4==k4

Solve[{p0,p1,p2,p3,p4},{a,b,c,d,e}]
Reduce[{p0,p1,p2,p3,p4},{a,b,c,d,e}]
Eliminate[{p0,p1,p2,p3,p4},{a,b,c,d,e}]
FindRoot[{p0,p1,p2,p3,p4},{a,-7822.5},{b,-1583.0},{c,-119.8060},{d,4.0183},{e,-0.0504}]