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:
is the integrated intensity (area) of the peak (parameter nameIntensity
) is the peak centre (parameter nameCentre
). is the parameterSkew
is the parameterExponent
(valid for ) is the parameterSigma
(valid for ) 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