Exact conditional distribution of a three-phase invariant in space group P1. IV. Further improvements of Cochran-like approximations.
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.
Shrager
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Physical Sciences Laboratory, Division of Computer Research and Technology, National Institutes of Health, Bethesda, Maryland 20982.
Shmueli
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Weiss
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D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods*; D003461:Crystallography / Q000379:methods*; D008432:Mathematical Computing; D008956:Models, Chemical; D011336:Probability