Asymptotic normality of coefficients of some polynomials related to Dowling lattices

Recently, we introduced two sequences of polynomials (Bn(x, y, z)) and (Fn(x, y, z)), which unify many familiar polynomials related to Dowling lattices, such as the Bell polynomials, the Dowling polynomials, the ordered Bell polynomials, the r-Bell polynomials and the r-Dowling polynomials. In this paper, we show the asymptotic normality of coefficients of Bn(x, y, z) and Fn(x, y, z). As applications, we obtain the asymptotic normality of coefficients of some polynomials related to Dowling lattices in a unified approach.