Edgeworth series probability distribution of intensity for spacegroup P21/c

Abstract

Abstract Based on the assumption that the structure factor components X = [unk] nj cos 2π(hxj + kyj + lZj )and Y = [unk] nj sin 2π(hxj + kyj + lzj ) obey a statistics given by a truncated Edgeworth series, the probability distribution for the standardised intensity P(Z) and the cumulative probability for the standardised intensity N(Z) for the spacegroup P21/c are calculated. Also N(z) for a structure containing heavy atoms has been derived. Two specific cases: 1) an all light atom structure and 2) a structure containing one or more heavy atoms have been considered. P + (E[unk]), the probability that E[unk] is positive has been calculated and a modified tangent formula developed in case (1).