Symmetry- and composition-dependent cumulative distributions of the normalized structure amplitude for use in intensity statistics

Centric and acentric cumulative distribution functions of the normalized structure amplitude, which explicitly account for the presence of outstandingly heavy atoms in crystals of any symmetry, have been derived. These cumulative distributions can now be readily evaluated for all triclinic, monoclinic and orthorhombic space groups, with the exceptions of Fdd2 and Fddd, and thus constitute an extension of the commonly employed cumulative distributions based on the Wilson statistics. Expected discrepancies between the distributions derived in this work and the corresponding Wilson-type distributions are illustrated, and their symmetry and composition dependence is discussed in view of relevant applications to intensity statistics.