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Mathematical structure of the Pearson VII function has been analyzed. It is shown that the Fourier transform of the Pearson VII function is proportional to the autocorrelation of the Gamma distribution probability density function, and any order of the cumulants of the Fourier transform are expressed by simple formulas. A convolution model based on Person VII function has been examined. It is possible to derive a Pearson VII model for the convolution of the Lorentzian function with the autocorrelation of the Gamma distribution probability function, but the super-Lorentzian profile could not be well reproduced, when the shape parameter is determined by the kurtosis of the Fourier transform. It is suggested that lower order cumulants of the Fourier transform should be treated with more importance.Possible extension of the Pearson VII function is also discussed.
粉末回折ピーク形状の PearsonVII 関数によるモデル化
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