  In this paper, we extend an existing scheme for numerically calculating the
probability of ruin of a classical Cram\'er--Lundberg reserve process having
absolutely continuous but otherwise general claim size distributions. We employ
a dense class of distributions that we denominate Erlangized scale mixtures
(ESM) and correspond to nonnegative and absolutely continuous distributions
which can be written as a Mellin--Stieltjes convolution $\Pi\star G$ of a
nonnegative distribution $\Pi$ with an Erlang distribution $G$. A distinctive
feature of such a class is that it contains heavy-tailed distributions.
  We suggest a simple methodology for constructing a sequence of distributions
having the form $\Pi\star G$ to approximate the integrated tail distribution of
the claim sizes. Then we adapt a recent result which delivers an explicit
expression for the probability of ruin in the case that the claim size
distribution is modelled as an Erlangized scale mixture. We provide simplified
expressions for the approximation of the probability of ruin and construct
explicit bounds for the error of approximation. We complement our results with
a classical example where the claim sizes are heavy-tailed.
