  Given a non-degenerate $(0,2)$-tensor field $h$ on a smooth manifold $M$, we
consider a natural generalized complex and a generalized product structure on
the generalized tangent bundle $TM\oplus T^*M$ of $M$ and we show that they are
$\nabla$-integrable, for $\nabla$ an affine connection on $M$, if and only if
$(M,h,\nabla)$ is a quasi-statistical manifold. We introduce the notion of
generalized quasi-statistical structure and we prove that any quasi-statistical
structure on $M$ induces generalized quasi-statistical structures on $TM\oplus
T^*M$. In this context, dual connections are considered and some of their
properties are established. The results are described in terms of
Patterson-Walker and Sasaki metrics on $T^*M$, horizontal lift and Sasaki
metrics on $TM$ and, when the connection $\nabla$ is flat, we define
prolongation of quasi-statistical structures on manifolds to their cotangent
and tangent bundles via generalized geometry. Moreover, Norden and Para-Norden
structures are defined on $T^*M$ and $TM$.
