  For classical discrete systems on periodic lattice under constant composition
x, we derive explicit expression of any-order moments for configurational
density of states (CDOS). The derived expression clarifies that any-order
moments can always be given by linear combination of the first-order moments,
whose coefficient depends on geometric information of lattice. The expression
enables us to exactly determine system-size (N) dependence of moments, where
analytic representation in terms of N and x is explicitly given up to
lower-order generalized moment. Validity of the derived expression is confirmed
by exact estimation of moments for binary system bcc with finite system size,
considering all possible atomic configuration.
