Abstract
In paper I of this series [Giacovazzo (1979). Acta Cryst. A35, 757-764] a tangent formula was obtained which is able to take into account uncertainty of the 'known' phases. In paper II [Cascarano, Giacovazzo, Burla, Nunzi & Polidori (1984). Acta Cryst. A40, 389-394] the asymptotical distribution of the statistic αh was derived when the r component vectors Gj exp (iθj) were distributed according to Von Mises distributions M(θj; ϕh, Gj). In the present paper this result is extended to the case in which the vectors Gj exp (iθj) are distributed according to a more general distribution M(θj; ϕh, βj). From the theoretical results a weighting scheme for the tangent procedure is derived which uses the first two moments of the αh distribution. The scheme has been implemented in the SIR program; applications to real structures are presented.
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