In this article, we study Codazzi-couples of an arbitrary connection ∇ with a nondegenerate 2-form ω, an isomorphism L on the space of derivation of ρ-commutative algebra A, which the important examples of isomorphism L are almost complex and almost paracomplex structures, a metric g that (g, ω,L) form a compatible triple. We study a statistical structure on ρ-commutative algebras by the classical manner on Riemannian manifolds. Then by recalling the notions of almost (para-)Kähler ρ-commutative algebras, we generalized the notion of Codazzi-(para-)Kähler ρ-commutative algebra as a (para-)Kähler (or Fedosov) ρ-commutative algebra which is at the same time statistical and moreover define the holomorphic ρ-commutative algebras.
