The probabilistic estimation of triplet invariants: the formula P₁₃

The second representation of a triplet invariant [Giacovazzo (1977). Acta Cryst. A33, 933-944] is a collection of special quintets. In the present paper, the triplet is embedded in many more additional quintets obtained in a special way by symmetry operations on the indices of the structure factors. The method of joint probability distribution functions has been used to derive a formula for estimating triplets via the information contained in the basis and in the cross terms of the quintet invariants. The P₁₀ formula [Cascarano, Giacovazzo, Camalli, Spagna, Burla, Nunzi & Polidori (1984). Acta Cryst. A40, 278-283] is a special case of the new formula, here called P₁₃. The new expression has been applied to practical cases.