Exact conditional distribution of a three-phase invariant in the space group P1. III. Construction of an improved...

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.