.. _func-Gaussian:

========
Gaussian
========

.. index:: Gaussian

Description
-----------

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

.. math:: \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
:math:`2\sqrt{2\ln 2}*\mbox{Sigma}`.

The integrated peak intensity for the Gaussian is given by
:math:`\mbox{height} * \mbox{sigma} * \sqrt{2\pi}`.

The uncertainty for the intensity is:
:math:`\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:

.. figure:: /images/GaussianWithConstBackground.png
   :alt: GaussianWithConstBackground.png

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