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It is assumed that a crystal structure in P{\bar 1} is fixed and that the 15 non-negative numbers R1, R2, R3, R4, R5; R12, R13, R14, R15, R23, R24, R25, R34, R35, R45 are also specified. The random vector (h, k, l, m, n) is assumed to be uniformly distributed over the subset of the fivefold Cartesian product W × W × W × W × W of reciprocal space W defined by |Eh| = R1, |Ek| = R2, |El| = R3, |Em| = R4, |En| = R5; (1) |Eh + k| = R12, |Eh + l| = R13, |Eh + m| = R14, |Eh + n| = R15, |Ek + l| = R23 |Ek + m| = R24, |Ek + n| = R25, |El + m| = R34, |El + m| = R35, |Em + n| = R45; (2) and h + k + l + m + n = 0. (3) Then the structure invariant (φ = φh + φk + φl + φm + φn, (4) as a function of the primitive random variables h, k, l, m, n, is itself a random variable, and its conditional probability distribution, given (1) and (2), is derived. The distribution yields reliable estimates for large numbers of quintets φ in terms of the 15 magnitudes (1) and (2).

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