This paper is a continuation of the work done by Deo et al. (Appl. Math. Comput. 273, 281–289, 2016), in which the authors have established some approximation properties of the Stancu–Kantorovich operators based on Pólya–Eggenberger distribution. We obtain some direct results for these operators by means of the Lipschitz class function, the modulus of continuity and the weighted space. Also, we study an approximation theorem with the aid of the unified Ditzian–Totik modulus of smoothness ωϕτ(f;t),0≤τ≤1 and the rate of convergence of the operators for the functions having a derivative which is locally of bounded variation on [0 , ∞). © 2017, Springer-Verlag Italia S.r.l.