  Object orientation provides a flexible framework for the implementation of
the convolution of arbitrary distributions of real-valued random variables.
  We discuss an algorithm which is based on the discrete Fourier transformation
(DFT) and its fast computability via the fast Fourier transformation (FFT). It
directly applies to lattice-supported distributions. In the case of continuous
distributions an additional discretization to a linear lattice is necessary and
the resulting lattice-supported distributions are suitably smoothed after
convolution.
  We compare our algorithm to other approaches aiming at a similar generality
as to accuracy and speed. In situations where the exact results are known,
several checks confirm a high accuracy of the proposed algorithm which is also
illustrated at approximations of non-central $\chi^2$-distributions.
  By means of object orientation this default algorithm can be overloaded by
more specific algorithms where possible, in particular where explicit
convolution formulae are available.
  Our focus is on R package distr which includes an implementation of this
approach overloading operator "+" for convolution; based on this convolution,
we define a whole arithmetics of mathematical operations acting on distribution
objects, comprising, among others, operators "+", "-", "*", "/", and "^".
