  We consider phase-type scale mixture distributions which correspond to
distributions of a product of two independent random variables: a phase-type
random variable $Y$ and a nonnegative but otherwise arbitrary random variable
$S$ called the scaling random variable. We investigate conditions for such a
class of distributions to be either light- or heavy-tailed, we explore
subexponentiality and determine their maximum domains of attraction. Particular
focus is given to phase-type scale mixture distributions where the scaling
random variable $S$ has discrete support --- such a class of distributions has
been recently used in risk applications to approximate heavy-tailed
distributions. Our results are complemented with several examples.
