Abstract
In this paper, we derive Chen inequality for statistical submanifold of statistical warped product manifolds R x (f) M. Further, we derive Chen inequality for Legendrian statistical submanifold in statistical warped product manifolds R x (f) M. We also provide some applications of derived inequalities in a statistical warped product manifold which is equivalent to a hyperbolic space. Moreover, we construct new examples of statistical warped product manifolds to support results.