Convolution between Gaus and power function

[Noor1]

Dear All
I have an alpha peak need to apply a proper fitting function, and because alpha peak is not well Gaussian peak. but rather a Gaussian + tail on the left.
I have created two fitting functions
Power for the tail range and Gaussian for the peak as follows

TF1 *fPower = new TF1("fPower","[0]*TMath::Power(x,(1/[1]))", 80,250); 
fPower->SetParameters(10000, 68); 
fPower->SetLineColor(kBlue);
f->Fit("fPower", "R"); 


TF1 *gausBi= new TF1("gausBi","gaus",200,1300);
gausBi->SetLineColor(kBlack);
f->Fit(gausBi, "R+");

Next step I am trying to formulate this in one function for the full range, or what refer to convolution.
so I build this new function and called the initial parameters as follows

TF1 *fPower_gausBi = new TF1("fPower_gausB", "fPower+gausBi", 80, 1200);
 Double_t par[5];
fPower->GetParameters(&par[0]);
gausBi->GetParameters(&par[2]);

fPower_gausB->SetParameters(par);
f->Fit(fPoisson_gausBi, "R+");

But this not make fitting in two ranges that’s why I get the wrong fitting curve (Red line).

any suggestion for the convolution process ??
fit.pdf (17.2 KB)

[moneta]

Hi,

Why not using the cristal ball function

Crystal Ball function

that is available in ROOT as

TF1 f1("f1","crystalball")

or as ROOT::Math::crystal_ball https://root.cern.ch/doc/v608/group__PdfFunc.html#ga6d2dcba56ea7438dab7e47e8c06c83f6

an example is available at

https://root.cern.ch/doc/v608/CrystalBall_8C.html

[Noor1]

Thank you for this suggestion, I tried crystalball function, but it did not work and because it is difficult to control the parameters I choose to do it manually by convolution between two functions.

thank you

[Wile_E_Coyote]

Try:

  TF1 *fPower_gausBi = new TF1("fPower_gausB", "(x < 222.) * fPower + (x >= 222.) * gausBi", 80., 1300.);

or:

  TF1 *fPower_gausBi = new TF1("fPower_gausB", "TMath::Min(fPower, gausBi)", 80., 1300.);

BTW. A sum of two functions is NOT their “convolution”.