  Information geometry is an important tool to study statistical models. There
are some important examples in statistical models which are regarded as warped
products. In this paper, we study information geometry of warped products. We
consider the case where the warped product and its fiber space are equipped
with dually flat connections and, in the particular case of a cone,
characterize the connections on the base space $\mathbb{R}_{>0}$. The resulting
connections turn out to be the $\alpha$-connections with $\alpha = \pm{1}$.
