General Purpose Convolution Algorithm in S4-Classes by means of FFT.
Abstract
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
and its fast computability via the Fast Fourier Transformation. 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.
Our focus is on \proglang{R} package \pkg{distr} which includes an
implementation of this approach. Several checks in situations where the exact
results are known confirm a high accuracy of the proposed algorithm.
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