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Some symmetric X-ray diffraction peaks can be approximated in shape by Pearson type VII distributions:
![y(x) = y_0[1 + (x - \bar x)^{2}/ma^2]^{-m}.](http://journals.iucr.org/j/issues/1977/01/00/a15317//teximages/a15317fd1.gif){kind=small}
This distribution is Cauchy for m = 1, modified Lorentzian for m = 2, and Gaussian for m = ∞. Some properties of the distribution and some illustrative applications are presented.
