We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzela, Dini and P. S. Alexandroff, as well as their statistical versions studied in [Caserta A., Di Maio G., Koeinac L. D. R., Statistical convergence in function spaces,. Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.] and [Caserta A., Kocinac L. D. R., On statistical exhaustiveness, Appl. Math. Lett. 25 (2012), no. 10, 1447-1451].