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We show that, for an affine submersion $\pi: \mathbf{M}\longrightarrow\mathbf{B}$ with horizontal distribution, $\mathbf{B}$ is a statisticalmanifold with the metric and connection induced from the statistical manifold$\mathbf{M}$. The concept of conformal submersion with horizontal distributionis introduced, which is a generalization of affine submersion with horizontaldistribution. Then proved a necessary and sufficient condition for$(\mathbf{M}, \nabla, g_M)$ to become a statistical manifold for a conformalsubmersion with horizontal distribution. A necessary and sufficient conditionis obtained for the curve $\pi \circ \sigma$ to be a geodesic of $\mathbf{B}$,if $\sigma$ is a geodesic of $\mathbf{M}$ for $\pi: (\mathbf{M},\nabla)\longrightarrow (\mathbf{B},\nabla^*) $ a conformal submersion with horizontaldistribution. Also, we obtained a necessary and sufficient condition for thetangent bundle $T\mathbf{M}$ to become a statistical manifold with respect tothe Sasaki lift metric and the complete lift connection.

Affine and Conformal Submersions with Horizontal Distribution and Statistical Manifolds