.. index:: Gaussian
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:
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