Re: [ROOT] Question on fitting with chi-squared

From: Nicolas de Sereville (deserevi@csnsm.in2p3.fr)
Date: Fri Nov 15 2002 - 12:12:57 MET


Hi Alexander,

I tried your small program and I obtain the following result of 0.3 as 
expected using ROOT from CVS of one week ago on RH7.2 :

root [0] TH1F* h1=new TH1F("h1","test",10,1,10)
root [1] h1->SetBinContent(3,1)
root [2] h1->SetBinContent(7,2)
root [3] h1->Fit("pol0","W")
 FCN=4.1 FROM MIGRAD    STATUS=CONVERGED      11 CALLS          12 TOTAL
                     EDM=1.0137e-24    STRATEGY= 1      ERROR MATRIX 
ACCURATE
  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
   1  p0           3.00000e-01   3.16228e-01  -0.00000e+00   6.36774e-12
<TCanvas::MakeDefCanvas>: created default TCanvas with name c1
(Int_t)0

Nicolas
 

Alexander Dietz wrote:

>Hello Rooters,
>
>as I know the chi-square method, used to estimate parameters, goes like
>this:
>
>
>chisquare=sum_{i=1}^N (x_i - y_i)^2/e_i
>
>
>with x_i being the value from a spectrum and y_i being the theoretical
>function depending on one or more parameters.
>To get the best-fitting values for the parameters this function must be
>minimized.
>Suppose to fit a constant y with fit-option 'w' (setting all errors to 1).
>Then the chisquare-value should be calculated like this:
>
>
>chisquare=sum_{i=1}^N (x_i - y)^2
>
>
>It is simple to calculate y for which this value is minimal:
>
>y=( sum_{i=1}^n x_i ) /n
>
>so y is simple the mean value of the data in the spectrum.
>
>I checked this with the following program:
>
>
>  TH1F* h1=new TH1F("h1","test",10,1,10);
>  h1->SetBinContent(3,1);
>  h1->SetBinContent(7,2);
>  h1->Fit("pol0","W");
>
>but what I get is a best-value of 1.5 instead of 0.3!
>It seems that ROOT ignores every channel with zero-content.
>
>Is ROOT ignoring channels with zero-contente and why?
>What can I do that ROOT gives the correct value?
>
>Cheers
>
>	Alexander Dietz
>
>
>  
>

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