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MathGroup Archive 2005

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Nonlinear Curve Fitting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53812] Nonlinear Curve Fitting
  • From: nilaakash at gmail.com (nilaakash)
  • Date: Fri, 28 Jan 2005 02:43:59 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Friends,
              I have tried to fit a nonlinear curve, but failed. I am
giving my points and it's curve equation is

    \!\(y = a \((1 - x\/c)\)\^b\)

Here a, b, c are fit parameters. My initial guess is like
   a =   0.3
   b =   0.2
   c = 385.2

data={{382.55, 0.112531}, {382.351, 0.113271}, {382.15, 0.115013},
{381.95,
    0.116646}, {381.749, 0.118108}, {381.549, 0.119477}, {381.352, 
    0.120815}, {381.15, 0.122088}, {380.95, 0.123275}, {380.75, 
    0.124776}, {380.55, 0.125688}, {380.35, 0.126676}, {380.15, 
    0.127719}, {379.95, 0.128744}, {379.75, 0.129687}, {379.549, 
    0.130706}, {379.35, 0.131595}, {379.149, 0.132522}, {378.95, 
    0.133465}, {378.75, 0.134297}, {378.55, 0.135198}, {378.35, 
    0.135965}, {378.15, 0.136919}, {377.95, 0.137599}, {377.749, 
    0.138507}, {377.55, 0.139172}, {377.35, 0.140088}, {377.15, 
    0.140695}, {376.95, 0.141593}, {376.75, 0.142154}, {376.55, 
    0.143089}, {376.35, 0.143644}, {376.149, 0.144522}, {375.95, 
    0.14509}, {375.75, 0.145836}, {375.55, 0.14655}, {375.35, 
    0.147098}, {375.15, 0.147927}, {374.95, 0.148362}, {374.749, 
    0.149214}, {374.55, 0.149868}, {374.35, 0.150402}, {374.15, 
    0.151099}, {373.949, 0.151528}, {373.75, 0.1524}, {373.55, 
    0.152919}, {373.35, 0.153435}, {373.15, 0.154261}, {372.95, 
    0.154473}, {372.75, 0.155232}, {372.55, 0.155874}, {372.35, 
    0.156397}, {372.149, 0.156851}, {371.949, 0.157775}, {371.75, 
    0.158082}, {371.55, 0.158616}, {371.349, 0.15936}, {371.15, 
    0.159811}, {370.95, 0.160188}, {370.75, 0.161122}, {370.55, 
    0.16138}, {370.35, 0.161574}, {370.15, 0.162232}, {369.949, 
    0.163392}, {369.751, 0.163124}, {369.55, 0.163277}, {369.35, 
    0.164757}, {369.15, 0.164471}, {368.95, 0.164512}, {368.75, 
    0.165126}, {368.55, 0.166819}, {368.35, 0.168995}, {368.15, 
    0.168555}, {367.95, 0.168609}, {367.75, 0.169652}, {367.55, 
    0.169828}, {367.35, 0.169679}, {367.15, 0.169972}, {366.95, 
    0.170693}, {366.751, 0.171106}, {366.55, 0.171399}, {366.35, 
    0.171651}, {366.15, 0.172006}, {365.95, 0.172645}, {365.75, 
    0.173137}, {365.55, 0.173136}, {365.35, 0.173773}, {365.15, 
    0.174123}, {364.95, 0.174443}, {364.75, 0.174802}, {364.55, 
    0.175113}, {364.35, 0.175806}, {364.15, 0.176169}, {363.95, 
    0.176401}, {363.75, 0.176578}, {363.55, 0.176953}, {363.35, 
    0.177432}, {363.15, 0.177765}, {362.95, 0.177845}, {362.75, 
    0.178067}, {362.55, 0.178569}, {362.35, 0.179083}, {362.15, 
    0.179272}, {361.95, 0.179384}, {361.75, 0.179777}, {361.551, 
    0.180256}, {361.349, 0.180579}, {361.15, 0.180718}, {360.95, 
    0.181023}, {360.75, 0.18146}, {360.55, 0.181936}, {360.35, 
    0.181999}, {360.151, 0.182136}, {359.95, 0.182558}, {359.75, 
    0.183018}, {359.55, 0.183377}, {359.35, 0.183487}, {359.15, 
    0.183709}, {358.95, 0.184118}, {358.75, 0.184511}, {358.55, 
    0.184856}, {358.35, 0.184902}, {358.15, 0.185134}, {357.95, 
    0.18549}, {357.75, 0.185944}, {357.55, 0.186194}, {357.35, 
    0.186338}, {357.15, 0.186497}, {356.95, 0.186801}, {356.75, 
    0.187286}, {356.55, 0.187679}, {356.35, 0.187856}, {356.15, 
    0.187953}, {355.95, 0.188292}, {355.75, 0.188656}, {355.55, 
    0.189001}, {355.35, 0.189234}, {355.15, 0.189379}, {354.95, 
    0.189551}, {354.75, 0.189823}, {354.549, 0.190173}, {354.35, 
    0.190491}, {354.15, 0.19072}, {353.95, 0.190911}, {353.75, 
    0.191116}, {353.55, 0.19133}, {353.35, 0.191617}, {353.15, 
    0.191903}, {352.95, 0.192179}, {352.75, 0.192324}, {352.55, 
    0.192525}, {352.35, 0.192726}, {352.15, 0.193037}, {351.95, 
    0.193273}, {351.75, 0.193512}, {351.55, 0.193766}, {351.35, 
    0.193925}, {351.151, 0.194099}, {350.95, 0.194293}, {350.75, 
    0.194514}, {350.55, 0.194769}, {350.35, 0.195005}, {350.15, 
    0.19527}, {349.95, 0.195444}, {349.75, 0.195603}, {349.55, 
    0.195743}, {349.35, 0.195977}, {349.15, 0.196241}, {348.95, 
    0.196497}, {348.75, 0.196661}, {348.55, 0.196848}, {348.35, 
    0.197031}, {348.15, 0.197189}, {347.95, 0.197359}, {347.75, 
    0.197566}, {347.55, 0.197798}, {347.35, 0.198015}, {347.15, 
    0.198241}, {346.95, 0.198459}, {346.75, 0.198643}, {346.55, 
    0.198803}, {346.35, 0.198968}, {346.15, 0.199108}, {345.95, 
    0.199294}, {345.75, 0.199527}, {345.55, 0.199761}, {345.35, 
    0.200008}, {345.15, 0.200202}, {344.95, 0.200311}, {344.75, 
    0.200481}, {344.55, 0.20064}, {344.35, 0.200819}, {344.15, 
    0.201037}, {343.95, 0.201279}, {343.75, 0.201518}, {343.551, 
    0.201718}, {343.35, 0.201888}, {343.15, 0.202039}, {342.95, 
    0.20219}, {342.75, 0.202339}, {342.55, 0.202529}, {342.35, 
    0.202706}, {342.15, 0.202881}, {341.95, 0.203091}, {341.75, 
    0.203274}, {341.55, 0.203498}, {341.35, 0.203684}, {341.15, 
    0.203875}, {340.95, 0.204088}, {340.75, 0.204272}, {340.55, 
    0.204489}, {340.35, 0.204658}, {340.15, 0.204811}, {339.95, 
    0.20495}, {339.75, 0.205069}, {339.55, 0.205247}, {339.35, 
    0.205441}, {339.15, 0.20562}, {338.95, 0.205837}, {338.75, 
    0.206019}, {338.55, 0.206215}, {338.35, 0.206369}, {338.15, 
    0.206536}, {337.95, 0.206684}, {337.75, 0.206844}, {337.55, 
    0.206981}, {337.35, 0.207116}, {337.15, 0.207285}, {336.95, 
    0.207474}, {336.75, 0.207668}, {336.55, 0.207867}, {336.35, 
    0.208033}, {336.15, 0.208205}, {335.95, 0.20837}, {335.75, 
    0.208516}, {335.552, 0.208639}, {335.35, 0.208779}, {335.15, 
    0.208952}, {334.95, 0.209164}, {334.75, 0.209378}, {334.55, 
    0.209519}, {334.35, 0.209637}, {334.15, 0.209792}, {333.95, 
    0.209865}, {333.75, 0.210065}, {333.55, 0.210288}, {333.35, 
    0.210415}, {333.15, 0.210534}, {332.95, 0.210705}, {332.75, 
    0.210876}, {332.55, 0.211065}, {332.35, 0.211264}, {332.15, 
    0.211427}, {331.95, 0.211577}, {331.75, 0.211715}, {331.55, 
    0.211856}, {331.35, 0.212039}, {331.15, 0.212206}, {330.949, 
    0.212384}, {330.75, 0.212548}, {330.55, 0.212727}, {330.35, 
    0.212883}, {330.15, 0.213023}, {329.95, 0.213175}, {329.75, 
    0.21334}, {329.55, 0.213508}, {329.35, 0.213678}, {329.15, 
    0.21385}, {328.95, 0.213997}, {328.75, 0.214134}, {328.55, 
    0.21429}, {328.35, 0.214471}, {328.15, 0.214574}, {327.95, 
    0.214685}, {327.75, 0.214832}, {327.55, 0.214982}, {327.35, 
    0.215121}, {327.15, 0.215276}, {326.949, 0.215443}, {326.75,
0.215625}}

Please help me to find out best a, b, c fit parameters.

Thanks.

nilaakash


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