TPeak

HOME > RUNNING GRSISORT > ANALYSIS > FITTING > TPEAK

TPeaks are used to fit photopeaks to a Gaussian + skewed gaussian. The background includes a step function. TPeaks inherit from TF1, which means they can be named, and can be written to TTrees and TFiles.

---

How To Use

TPeaks can be created as follows:

TPeak *peak = new TPeak(centroid, low_range, high_range);

To fit the TPeak, call:

peak->Fit(histogram);

where histogram is the TH1* attempting to be fit. You can also use the same options as when fitting a TF1. For example,

peak->Fit(histogram,"+");

to add the TPeak to the histogram.

Once the TPeak is fitted, you can call

peak->Print();

To see the basic properties of the TPeak

   Name:        Chan1173_1160_to_1190
   Centroid:    1173.172270 +/- 0.005742
   Area:          1885626.302501 +/- 1409.848616

Or, to see more properties, such as the value and uncertainty in each parameter, use the option Print("+").

Fitting Technique

One should always fit peaks using the proper statistical model. Gamma-rays are detected following a Poisson probability distribution. Therefore, when fitting a standard gamma ray spectrum, one should fit the peak using a maximum likelihood distribution. If background is subtracted, one is left with the difference of two Poisson distributed data sets, which is no longer a Poisson distributed data set. Thus, one would prefer to use least-squares fitting in this scenario. TPeak accommodates for this using a default maximum-likelihood fitting flag. To see what the current status of the flag is use TPeak::GetLogLikelihoodFlag();. To set the status of the flag, use TPeak::SetLogLikelihoodFlag(true); to turn maximum likelihood on and TPeak::SetLogLikelihoodFlag(false); to turn change it to least-squares fitting. It defaults to on.

Parameters

The first time a TPeak is fit, the parameters are initialized based on the histogram passed to the TPeak::Fit function. When a TPeak is created, the parameters are uninitialized. The names of the paramters are as follows:

• "Height": The height of the unskewed gaussian
• "centroid": The centroid of the unskewed gaussian
• "sigma": The width of the unskewed gaussian
• "beta": The "skewedness" of the skewed gaussian
• "R": The relative height of the skewed gaussian
• "step": The size of the step function in the background
• "A": The constant part of the background
• "B": The linear part of the background
• "C": The quadratic part of the background
• "bg_offset": The offset in the background in the x direction

To fix a particular component of the TPeak, for example, the width to 1.0, use:

peak->FixParameter(GetParNumber("sigma"),1.00);

To Release the paramater use:

peak->ReleaseParameter(GetParNumber("sigma"));

and to set the paramater to an initial value use:

peak->SetParameter("sigma",1.00);

which maintains its fixed/freeness.