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Gaussian

Description

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

\[\mbox{Height}*\exp \left( -0.5*\frac{(x-\mbox{PeakCentre})^2}{\mbox{Sigma}^2} \right)\]

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:

GaussianWithConstBackground.png

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