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fitting data with equation

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sarah
sarah 2015-5-29
评论： Star Strider 2015-5-30
Hi guys, so I have alot of experimental data in column matrix y. And I want to use the equation below to find the best fit for my data y. This means have constant b adjusted with x varying, I know that x typically ranges from 1 to 5 with y and b ranges from 0 to 2.
I'm thinking of using a double loop. Would anyone give me tips on how to solve for it effectively? Thanks in advance. The equation is:
y= (1-0.05*x^(b))/(1-0.05*x^b)^2

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Star Strider
Star Strider 2015-5-29
I would use a nonlinear curve fitting function such as nlinfit, lsqcurvefit (or fminsearch indirectly).
However if your (x,y)>0, are not noisy, y>1, and you want an estimate of ‘b’, this might work:
b = log(20*(1-1./y))./log(x);
Otherwise, use a nonlinear parameter estimation routine.
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sarah
sarah 2015-5-30
And may I ask how did you derive this expression? Thanks
Star Strider
Star Strider 2015-5-30
Sure!
y = (1-0.05*x^b)/((1-0.05*x^b)^2
(1/y) = 1-0.05*x^b
(1-(1/y))*20 = x^b
x = ((1-(1/y))*20)^(1/b)
Then vectorise it to do the calculation:
x = ((1-(1./y))*20).^(1./b);

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