The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P(1)over-bar case

The joint probability distribution function method has been developed in P (1) over bar for reflections with rational indices. The positional atomic p arameters are considered to be the primitive random variables, uniformly di stributed in the interval (0,1), while the reflection indices are kept fixe d. Owing to the rationality of the indices, distributions like P(F-p1, F-p2 ) are found to be useful for phasing purposes, where p(1) and p(2) are any pair of vectorial indices. A variety of conditional distributions like P(/F -p1/ \ /F-p2/), P(/F-p1/ /F-p2), P(phi(p1) / /F-p1/, F-p2) are derived, whi ch are able to estimate the modulus and phase of F-p1 given the modulus and /or phase of F-p2. The method has been generalized to handle the joint prob ability distribution of any set of structure factors, be. the distributions P(F-1, F-2, ..., Fn+1), P(/F-1/ /F-2, ..., Fn+1) and P(phi(1)/ /F/(1), F-2 , ..., Fn+1) have been obtained. Some practical tests prove the efficiency of the method.