The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1 case

The joint probability distribution function method has been developed in P1 for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F_p1, F_p2) are found to be useful for phasing purposes, where p₁ and p₂ are any pair of vectorial indices. A variety of conditional distributions like P(|F_p1| | |F_p2|), P(|F_p1| |F_p2), are derived, which 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 probability distribution of any set of structure factors, i.e. the distributions P(F₁, F₂,..., F_n+1), P(|F₁| |F₂,..., F_n+1) and P(₁| |F|₁, F₂,..., have been obtained. Some practical tests prove the efficiency of the method.