Dear Experts:
Hi, i encountered a problem of obtaining the peak position from the convolution PDF.
For example, i am using a Landau*Gauss convolution pdf to fit the histogram.
and by lgpdf->getVariables(), i can get the peak position of the landau pdf.
But this is different from the actual peak of the convoluted pdf.
My question is how to obtain the REAL peak position, and the error of it ?
any hints will be appreciate
Thank you in advanced !
Hi,
Assuming you have the Gaussian mean already fixed to zero, this happens
because the ‘mean’ parameter of TMath::Landau is only an approximation
of the MPV of the Landau (see earlier ROOT Forum thread on this issue here
root.cern.ch/phpBB2/viewtopic.php?p=29116)
To numerically find the function maximum you can do this following
RooAbsReal* dldx = landau->derivative(x) ;
Double_t xpeak ;
Bool_t ok = RooBrentRootFinder(RooRealBinding(*dldx,x)).findRoot(xpeak,xmin,xmax,0.) ;
where landau is your landau function (or your convolution, but given that these should
give the same answer, the calculation on the plain landau should be faster), x is
your observable and xmin,xmax are the minimum and maximum of x (or some smaller range that you are confident brackets the true peak position). The numerically found
peak value will be stored in xpeak.
Wouter
[quote=“Wouter Verkerke”]Hi,
Assuming you have the Gaussian mean already fixed to zero, this happens
because the ‘mean’ parameter of TMath::Landau is only an approximation
of the MPV of the Landau (see earlier ROOT Forum thread on this issue here
root.cern.ch/phpBB2/viewtopic.php?p=29116)
To numerically find the function maximum you can do this following
RooAbsReal* dldx = landau->derivative(x) ;
Double_t xpeak ;
Bool_t ok = RooBrentRootFinder(RooRealBinding(*dldx,x)).findRoot(xpeak,xmin,xmax,0.) ;
where landau is your landau function (or your convolution, but given that these should
give the same answer, the calculation on the plain landau should be faster), x is
your observable and xmin,xmax are the minimum and maximum of x (or some smaller range that you are confident brackets the true peak position). The numerically found
peak value will be stored in xpeak.
Wouter[/quote]
Hi, Thank you very much for your reply.
actually, the peak of the convoluted pdf. is different from the peak of the Landau, because of the gaussian smear effect, as you can see from the attched image.
any way , i take your method and it works very well. now i get three different value associating the MOP:
the one from mean landau:1.14149
the one from the derivative of landau:1.13126
and the one from the derivative of the convoluted pdf.: 1.21194
they seems to be agree very well, given the problem of mean landau you metioned.
Thank you very much !
