$$\renewcommand\AA{\unicode{x212B}}$$

# 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:

## 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