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how to find parameter heligman pollard model

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zul karnaen
zul karnaen on 5 Apr 2011
Closed: Sabin on 19 Dec 2022
i have question to every body....this is my project in college.. i have a problem about non-linear least square..and i working in matlab.. i have data
x1=[0;1;5;10;15;20;25;30;35;40;45;50;55;60;65;70;75];
ydata=[0.00859 0.001714 0.001466 0.001308 0.00381 0.005388 0.005978 0.00673 0.009336 0.014156 0.021598 0.034274 0.05383 0.08526 0.136546 0.21604 0.329148];
and my function is..
y=((b1.^((x+b2).^b3))+(b4.*exp(-b5.*(log(x./b6)).^2))+(b7.*(b8.^x)))/(1+((b1.^((x+b2).^b3))+(b4.*exp(-b5.*(log(x./b6)).^2))+(b7.*(b8.^x))));
how to find parameter
b1,b2....b8????
and i have been try it..to find parameter b1,b2....b8..this is my m.file
syms x y b1 b2 b3 b4 b5 b6 b7 b8 real
yduga=((b1.^((x+b2).^b3))+(b4.*exp(-b5.*(log(x./b6)).^2))+(b7.*(b8.^x)))/(1+((b1.^((x+b2).^b3))+(b4.*exp(-b5.*(log(x./b6)).^2))+(b7.*(b8.^x))));
r=y-yduga;
J=[diff(r,b1) diff(r,b2) diff(r,b3) diff(r,b4) di...ff(r,b5) diff(r,b6) diff(r,b7) diff(r,b8)];
c1(1)=?
c2(1)=?
c3(1)=?
c4(1)=?
c5(1)=?
c6(1)=?
c7(1)=?
c8(1)=?
for i=2:10
t=[c1(i-1) c2(i-1) c3(i-1) c4(i-1) c5(i-1) c6(i-1) c7(i-1) c8(i-1)]
xdata=[1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75];
ydata=[0.001714 0.001466 0.001308 0.00381 0.005388 0.005978 0.00673 0.009336 0.014156 0.021598 0.034274 0.05383 0.08526 0.136546 0.21604 0.329148];
rr=subs(r,{b1 b2 b3 b4 b5 b6 b7 b8},[t]);
rrr=subs(rr,{x y},{xdata ydata});
JJ=subs(J,{b1 b2 b3 b4 b5 b6 b7 b8},[t]);
JJJ=subs(JJ,{x},{xdata});
d=inv(JJJ'*JJJ)*(-1)*JJJ'*rrr;
beta=plus(t',d)
c1(i)=beta(1)
c2(i)=beta(2)
c3(i)=beta(3)
c4(i)=beta(4)
c5(i)=beta(5)
c6(i)=beta(6)
c7(i)=beta(7)
c8(i)=beta(8)
end
i using Gauss-newton method, but until this time i can't find parameter b1,b2..b8..maybe my problem is about starting value, but i dont know....?? i hope u all can help me thanks a lot....

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