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In this paper we consider, how to find the marginal distributions of crossing time and renewal numbers related with two poisson processes by using probability arguments. The obtained results show that the one-dimension marginal distributions are N+1 order PH-distributions.
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Talpur, M. G. H., & Ilyas, R. M. (2006). The Marginal Distributions of a Crossing Time and Renewal Numbers Related with Two Poisson Processes are as Ph-Distributions. Pakistan Journal of Statistics and Operation Research, 2(1), 27-34. https://doi.org/10.18187/pjsor.v2i1.83