caa a22 4500 475793021 CHVBK 20180406123715.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/s001840050048 doi (NATIONALLICENCE)springer-10.1007/s001840050048 On a study of the exponential and Poisson characteristics of the Poisson process [Elektronische Daten] [Wen-Jang Huang, Wen-Ching Chang] 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)). Springer-Verlag Berlin Heidelberg, 2000 Key words: Characterization nationallicence exponential distribution nationallicence Poisson distribution nationallicence Poisson process nationallicence renewal process nationallicence Huang Wen-Jang Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, R.O.C. (e-mail: huangwj@math.nsysu.edu.tw), TW aut Chang Wen-Ching Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, R.O.C. (e-mail: huangwj@math.nsysu.edu.tw), TW aut https://doi.org/10.1007/s001840050048 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840050048 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Huang Wen-Jang Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, R.O.C. (e-mail: huangwj@math.nsysu.edu.tw), TW aut NATIONALLICENCE 700 1- Chang Wen-Ching Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, R.O.C. (e-mail: huangwj@math.nsysu.edu.tw), TW aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer