  In this paper, we generalize the dualistic structures on warped product
manifolds to the dualistic structures on generalized warped product manifolds.
we develop an expression of curvature for the connection of the generalized
warped product in relation to those corresponding analogues of its base and
fiber and warping functions. we show that the dualistic structures on the base
$M_{_1}$ and the fiber $M_{_2}$ induces a dualistic structure on the
generalized warped product $M_1\times M_2$ and conversely, moreover,
$(M_{_1}\times M_{_1},G_{_{f_{_1}f_{_2}}})$ or $(M_{_1}\times
M_{_1},\tilde{g}_{_{f_{_1}f_{_2}}})$ is statistical manifold if and only if
$(M_{_1},g_{_1})$ and $(M_{_1},g_{_1})$ are. Finally, Some interesting
consequences are also given.
