Comparison of Methods for Evaluation of the Convolution of Two Compound R 1 Distributions

In the present paper we compare four methods for evaluating the convolution of two compound R 1 distributions by counting the numbers of elementary algebraic operations required. Two of the methods are applicable in general, whereas the remaining two are restricted to the case when the two compound distributions have the same severity distribution. This case is discussed separately. We consider in particular the special case when this common severity distribution is concentrated in one, that is, evaluation of the convolution of two R 1 distributions.