title: Application of maximum likelihood to direct methods: the probability density function of the triple-phase sums. XI.
abstract: The maximum-likelihood method is applied to direct methods to derive a more general probability density function of the triple-phase sums which is capable of predicting negative values. This study also proves that maximization of the origin-free modulus sum function S yields, within the limitations imposed by the assumed approximations, the maximum-likelihood estimates of the phases. It thus represents the formal theoretical justification of the S function that was initially derived from Patterson-function arguments [Rius (1993). Acta Cryst. A49, 406-409].
authors.affiliation: Institut de Ciència de Materials de Barcelona (CSIC), Campus de la UAB, 08193-Bellaterra, Catalunya, Spain. jordi.rius@icmab.es
authors.forename: Jordi
authors.initials: J
authors.lastname: Rius