On a study of the exponential and Poisson characteristics of the Poisson process | Zendy

WenJang Huang | Zendy; WenChing Chang | Zendy

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On a study of the exponential and Poisson characteristics of the Poisson process

Author(s) -

WenJang Huang,

WenChing Chang

Publication year - 2000

Publication title -

metrika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.728

H-Index - 40

eISSN - 1435-926X

pISSN - 0026-1335

DOI - 10.1007/s001840050048

Subject(s) - compound poisson process , mathematics , poisson distribution , poisson process , renewal theory , exponential function , counting process , process (computing) , poisson regression , combinatorics , statistics , mathematical analysis , computer science , population , demography , sociology , operating system

. 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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