Abstract.
Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations of the Poisson process as a renewal process. More precisely, let γt be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γt)=E 2 (γt),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)).
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Received: August 1999
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Huang, WJ., Chang, WC. On a study of the exponential and Poisson characteristics of the Poisson process. Metrika 50, 247–254 (2000). https://doi.org/10.1007/s001840050048
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DOI: https://doi.org/10.1007/s001840050048