  In 1972 Delange observed in analogy of the classical Erd\H os-Wintner theorem
that $q$-additive functions $f(n)$ has a distribution function if and only if
the two series $\sum f(d q^j)$, $\sum f(d q^j)^2$ converge. The purpose of this
paper is to provide quantitative versions of this theorem as well as
generalizations to other kinds of digital expansions. In addition to the
$q$-ary and Cantor case we focus on the Zeckendorf expansion that is based on
the Fibonacci sequence, where we provide a sufficient and necessary condition
for the existence of a distribution function, namely that the two series $\sum
f(F_j)$, $\sum f(F_j)^2$ converge (previously only a sufficient condition was
known).
