General purpose convolution algorithm in S4 classes by means of FFT

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 fast fourier transform. 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 for approximations of non-central χ2 distributions. by means of object orientation this default algorithm is overloaded by more specific algorithms where possible,in particular where explicit convolution formulae are available. our focus is on r package distr which implements this approach,overloading operator + for convolution; based on this convolution,we define a whole arithmetics of mathematical operations acting on distribution objects,comprising operators +,-,*,/,and ^. © 2014,american statistical association. all rights reserved.