On the Difference between the Concepts "Compound" and "Composed" Poisson Processes

In the discussion in the ASTIN Colloquium 1962, which followed my lecture on the numerical evaluation of the distribution functions defining some compound Poisson processes, a remark was made, which drew my attention to the paper quoted here below under reference number (I), On composed Poisson distributions I. As I have the impression that this remark may induce some confusion of the terms "compound" and "composed", the more as the same French word (composed) is used for the two terms, a comparison between the two kinds of processes shall be made.