A point process N is given, which is known to be the superposition of two independent renewal processes. Can it be deduced from the knowledge of the superposition alone what the distribution functions driving the renewal process are? Clearly the answer is no if the two renewal processes are Poisson. Apart from this special case, and under the additional assumption of analyticity of densities, it is proven that the answer is yes. This result answers a question posed by Neuts and Meier-Hellstern about superpositions of phase-type renewal processes. Using similar techniques, examples are given showing that the well-known inclusion relations between certain families of point processes based on Markov chains are strict.
