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The properties of frequency distributions of inter-event intervals in the pooled output of several point processes where the points can be distinguished are investigated. In the case where the component processes are mutually independent, the p.d.f.'s of inter-event intervals in the pooled output are explicitly expressed, and the reciprocal relations on the p.d.f.'s and on the numbers of inter-event intervals are revealed.
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Yoshifusa Ito (1977) studied this question.
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