  Let $F$ be the cumulative distribution function (CDF) of the base-$q$
expansion $\sum_{n=1}^\infty X_n q^{-n}$, where $q\ge2$ is an integer and
$\{X_n\}_{n\geq 1}$ is a stationary stochastic process with state space
$\{0,\ldots,q-1\}$. In a previous paper we characterized the absolutely
continuous and the discrete components of $F$. In this paper we study special
cases of models, including stationary Markov chains of any order and stationary
renewal point processes, where we establish a law of pure types: $F$ is then
either a uniform or a singular CDF on $[0,1]$. Moreover, we study mixtures of
such models. In most cases expressions and plots of $F$ are given.
