International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B. ch. 2.1, p. 196
Section 2.1.5.5. Relation to distributions of I^{a}School of Chemistry, Tel Aviv University, Tel Aviv 69 978, Israel, and ^{b}St John's College, Cambridge, England 
When only the intrinsic probability distributions are being considered, it does not greatly matter whether the variable chosen is the intensity of reflection (I), or its positive square root, the modulus of the structure factor , since both are necessarily real and nonnegative. In an obvious notation, the relation between the intensity distribution and the structurefactor distribution is or Statistical fluctuations in counting rates, however, introduce a small but finite probability of negative observed intensities (Wilson, 1978a, 1980a) and thus of imaginary structure factors. This practical complication is treated in IT C (2004, Parts 7 and 8 ).
Both the ideal centric and acentric distributions are simple members of the family of gamma distributions, defined by where n is a parameter, not necessarily integral, and is the gamma function. Thus the ideal acentric intensity distribution is and the ideal centric intensity distribution is The properties of gamma distributions and of the related beta distributions, summarized in Table 2.1.5.1, are used in Section 2.1.6 to derive the probability density functions of sums and of ratios of intensities drawn from one of the ideal distributions.

References
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