$$

Gaussian

Description

A Gaussian function (also referred to as a normal distribution) is defined as:

$$\text{Height}\ast \exp (-0.5\ast \frac{(x-\text{PeakCentre}{)}^2}{{\text{Sigma}}^2})$$

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 $2\sqrt{2\ln 2}\ast \text{Sigma}$.

The integrated peak intensity for the Gaussian is given by $\text{height}\ast \text{sigma}\ast \sqrt{2\pi }$.

The uncertainty for the intensity is: $\text{intensity}\ast \sqrt{{\left(\frac{\delta \text{height}}{\text{height}}\right)}^2+{\left(\frac{\delta \text{sigma}}{\text{sigma}}\right)}^2}$.

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