title: Exact conditional distribution of a three-phase invariant in space group P1. IV. Further improvements of Cochran-like approximations.
abstract: A new approximate method of computing the conditional probability density function (c.p.d.f.) of a three-phase invariant is investigated, the results being compared to accurate calculations [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361-367]. A direct dependence on N, the number of atoms in the unit cell, is incorporated into the new approximation and its performance in the equal-atom case appears to be excellent over a large range of N values. The polynomial approximation of the recently published method [Posner, Shmueli & Weiss (1993). Acta Cryst. A49, 260-265] has been improved in both accuracy and range.
authors.affiliation: Physical Sciences Laboratory, Division of Computer Research and Technology, National Institutes of Health, Bethesda, Maryland 20982.
authors.forename: R I
authors.initials: RI
authors.lastname: Shrager
authors.forename: U
authors.initials: U
authors.lastname: Shmueli
authors.forename: G H
authors.initials: GH
authors.lastname: Weiss
mesh_terms: D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods*; D003461:Crystallography / Q000379:methods*; D008432:Mathematical Computing; D008956:Models, Chemical; D011336:Probability