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PearsonIV¶
Description¶
The PearsonIV peak shape is used to fit the prompt pulse in time-of-flight spectra. It differs from the traditional definition of the PearsonIV distribution [1] in that the Mantid definition has the peak centre (Centre`) shifted so that it coincides with the peak maximum.
The function is defined as .. math:: frac{I}{sigma}Nleft[1 + left(frac{x - lambda - nusigma/(2m)right)^{2}}{sigma}right]^{-m}expleft(-nu arctan(frac{x - lambda - nusigma/(2m)}{sigma}) right)
where:
\(I\) is the integrated intensity (area) of the peak (parameter name
Intensity
)\(\lambda\) is the peak centre (parameter name
Centre
).\(\nu\) is the parameter
Skew
\(m\) is the parameter
Exponent
(valid for \(m > 0.5\))\(\sigma\) is the parameter
Sigma
(valid for \(\sigma > 0\))\(N = \frac{2^{2m-2}\left|\Gamma(m+i\nu/2)\right|^2}{\pi\sigma\Gamma(2m-1)}\) is the normalisation
Attributes (non-fitting parameters)¶
Name |
Type |
Default |
Description |
---|---|---|---|
CentreShift |
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
Intensity |
1.0 |
Area under the peak. |
Centre |
0.0 |
Position of the peak maximum (note this differs from the usual definition of the PearsonIV - for which the ‘location’ parameter coincides with the maximum only for skew=0). |
Sigma |
1.0 |
One of the parameters controlling the width of peak (valid for Sigma > 0) - increasing Sigma increases the FWHM. |
Exponent |
1.5 |
One of the parameters controlling the width of peak (valid for Exponent > 0.5) - increasing Exponent decreases the FWHM. |
Skew |
0.0 |
Parameter determining the skew/asymmetry of the peak - a negative value of Skew produces a peak with centre of mass at larger x value than the peak centre/maximum. |
References¶
Categories: FitFunctions | General
Source¶
Python: PearsonIV.py