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Gaussian¶
Description¶
A Gaussian function (also referred to as a normal distribution) is defined as:
where
Height - height of peak
PeakCentre - centre of peak
Sigma - Gaussian width parameter
Note that the FWHM (Full Width Half Maximum) of a Gaussian equals \(2\sqrt{2\ln 2}*\mbox{Sigma}\).
The integrated peak intensity for the Gaussian is given by \(\mbox{height} * \mbox{sigma} * \sqrt{2\pi}\).
The uncertainty for the intensity is: \(\mbox{intensity} * \sqrt{\left(\frac{\delta \mbox{height}}{\mbox{height}}\right)^2 + \left(\frac{\delta \mbox{sigma}}{\mbox{sigma}}\right)^2}\).
The figure below illustrate this symmetric peakshape function fitted to a TOF peak:
Properties (fitting parameters)¶
Name |
Default |
Description |
|---|---|---|
Height |
0.0 |
Height of peak |
PeakCentre |
0.0 |
Centre of peak |
Sigma |
0.0 |
Width parameter |
Categories: FitFunctions | Peak | Muon\MuonModelling
Source¶
C++ header: Gaussian.h
C++ source: Gaussian.cpp