equation: R(X, Y )Z = h(Y, Z)SX − h(X, Z)SY, Codazzi equations: (∇X h)(Y, Z) + h(Y, Z)τ(X) −(∇Y h)(X, Z) + h(X, Z)τ(Y ) = −h(T ∇(X, Y ), Z), (∇X S)(Y ) + τ(Y )SX − (∇Y S)(X) − τ(X)SY = −S(T ∇(X, Y )), Ricci equation: h(X, SY ) − (∇X τ)(Y ) − h(Y, SX) + (∇Y τ)(X) = τ(T ∇(X, Y )). Proposition 5.4 (Haba (2020)) M : simply connected. ∇ : an affine connection, S : a (1, 1)-tensor field h : a (0, 2)-tensor field, τ : a 1-form ∇, h, S and τ satisfy fundamental equations =⇒ ∃{ω, ξ} : an affine distribution which induces ∇, h, S and τ. Theorem 5.5 (Haba (2020)) (1) {ω, ξ} : nondegenerate, equiaffine =⇒ (M, ∇, h) : 1-conformally partially flat quasi statistical manifold. (2) {ω, ξ} : symmetric, nondegenerate, equiaffine =⇒ (M, ∇, h) : 1-conformally partially flat SMAT. If M is simply connected, the converses also hold