In this paper, we obtain the classifications of \(\beta \) -Kenmotsu statistical structures of constant \(\phi \) -sectional curvature on \(\beta \) -Kenmotsu space forms. Our results show that such \(\beta \) -Kenmotsu statistical structures on a \(\beta \) -Kenmotsu space form with dimension greater than 3 must be almost-trivial; on a 3-dimensional \(\beta \) -Kenmotsu space form, in addition to the almost-trivial \(\beta \) -Kenmotsu statistical structure, there exist other \(\beta \) -Kenmotsu statistical structures which satisfy the constant \(\phi \) -sectional curvature condition. These results generalize and improve the corresponding results for Kenmotsu statistical manifolds Jiang et al. (Hacet J Math Stat 51(3):800–816, 2022) as well as cosymplectic statistical manifolds Yan et al. (J Geom Phys 196:105076, 2024). Before obtaining these main results on \(\beta \) -Kenmotsu statistical structures, we also obtain the expression for the curvature tensor of the \(\beta \) -Kenmotsu space form in terms of Riemannian geometry, and many examples are given by using warped products.
