Posner Y, Shmueli U, Weiss G H
School of Chemistry, Tel Aviv University, Israel.
Acta Crystallogr A. 1993 Mar 1;49 ( Pt 2):260-5. doi: 10.1107/s0108767392005506.
An exact representation of the accurately computable conditional probability density function (c.p.d.f.) of the three-phase invariant for the space group P1 was developed in paper I of this series [Shmueli, Rabinovich & Weiss (1989). Acta Cryst. A45, 361-367]. The computation of this function is too time-consuming for it to be of practical value. It is therefore desirable to find simple approximations based on the exact result that may be more accurate than the familiar Cochran approximation or its extensions. One such approximation, presented here, has the same functional form as the Cochran approximation but with a modified parameter in place of that appearing in Cochran's distribution. Some of the numerical procedures used in the estimation of this modified parameter are also discussed.
本系列论文I [Shmueli、Rabinovich和Weiss（1989年）。《晶体学报》A45卷，361 - 367页] 给出了空间群P1的三相不变量的精确可计算条件概率密度函数（c.p.d.f.）的精确表示。该函数的计算耗时过长，不具有实际应用价值。因此，希望基于精确结果找到比常用的 Cochr an近似或其扩展更准确的简单近似方法。本文提出的一种此类近似方法，其函数形式与 Cochr an近似相同，但用一个修改后的参数替代了 Cochr an分布中的参数。还讨论了用于估计此修改后参数的一些数值方法。
