Compute uncertainty of integral of a component of a TF1

[canigia]

Hi,

I am wondering whether there is functionality in standard ROOT (not RooFit) to compute the uncertainty of a component of a TF1. E.g. if fitting a function TF1 f1(“f1”,“gaus(0)+pol2(3)”) to a spectrum, I’d like to get the integral and its uncertainty only for the gaus(0) component.

If there is no function available, how can I properly can do this myself?

Another related question: If using a signal component, where the “amplitude” parameter already represents the integral (like it should be the case for gausn), can I assume that the uncertainty of the integral is correctly represented by the uncertainty of this fit parameter?

Thanks,
Klaus

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[Wile_E_Coyote]

TH1F variable bin width

Using the "60Codata.txt" file (attached in another post here), try this: { const Bool_t fit_with_fixed_background = kFALSE; // kFALSE or kTRUE const char *filename = "60Codata.txt"; TGraph *g0 = new TGraph(filename, "%lg %lg %*lg"); // X axis = channels g0->SetTitle("g0;Channel number;Energy"); // energy calibration TGraph *g1 = new TGraph(filename, "%lg %*lg %lg"); // X axis = channels g1->SetTitle("g1;Channel number;Counts"); TGraph *g2 = new TGraph(filename, "%*lg %lg %lg");…

Integral Error in Signal

The original example uses “pol1(3)” so there are 2 parameters, but you use “pol2(3)” so you have 3 parameters. That means that you need to change “3, 4” into “3, 5” in all relevant places. In the first macro therein, you also need to add two lines (needed when “fit_with_fixed_background” = “kTRUE”): // ... f1->FixParameter(4, f1->GetParameter(4)); // this line already exists f1->FixParameter(5, f1->GetParameter(5)); // ... f2->FixParameter(4, f2->GetParameter(4)); // this l…

Facing Problem while fitting

The first parameter of “gaus” is the “peak’s height” while the first parameter of “gausn” is the “peak’s area”. In both cases, the second parameter is the “peak’s mean” (i.e. the “peak’s position”). { TGraph *g = new TGraph("eu_gu_1.dat"); // g->Sort(); // just a precaution TF1 *f1 = new TF1("f1", "gausn(0) + pol1(3)", 400., 435.); // linear background f1->SetParameters(14000., 415., 2., 0., 0.); g->Fit("f1", "BR+"); TF1 *f2 = new TF1("f2", "gausn(0) + pol1(3)", 1160., 1200.); f2…

[canigia]

Hi,

thanks for the quick answer! Some follow-up questions:

• according to the example electronPionID.C in the 2nd post, the integral error of the signal seems to be extracted only from the signal parameters covariance, right?
  TMatrixD c1g = c1.GetSub(0, 2, 0, 2);
  This seems to neglect correlations of background parameters with signal parameters. I.e. I can well imagine, that changing the background shape has impact on the signal integral. Or am I wrong?

• you 3rd quote seems to address my 2nd question about, whether e.g. the error of par. 0 of a gausn is already representing the integral error of the signal component. But it didn’t seem to answer it but just points out the difference between gaus and gausn. Or did I miss something?

Best, Klaus

[Wile_E_Coyote]

Run both macros from the first link using “fit_with_fixed_background” = “use_partial_covariance” = “kFALSE”. Then set both variables to “kTRUE” and run both macros again. Compare the obtained results.

See also: Wikipedia → Covariance matrix → Partial covariance matrix