A study of nonhomogeneous Poisson process and record value

• Main Authors: Hwang, Yi Ting, 黃怡婷
• Other Authors: Huang, Wen Jang
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/86906220795856705267

碩士 === 國立中山大學 === 應用數學研究所 === 81 === In this thesis we discuss some characterizations related to nonhomogeneous Poisson process and record values. Let {N(t), t .gtoreq 0} be a nonhomogeneous Poisson process with {S_n, n .gtoreq 1} being the sequence of arrival times, .gamma_t and .delta_t being the residual life and current life at t, respectively. Using some properties related to {S_n,n .gtoreq 1},.gamma_t or .delta_t, we characterize the homogeneous Poisson process among the class of nonhomogeneous Poisson process. This part is discussed in Chapter I. Based on a sequence of independent and identically distributed random variables { X_n, n .gtoreq 1} with a common distribution function F, we define the sequence of upper record values {S_n, n .gtoreq 1}. It is known that the process {N(t), t .gtoreq 0}, where N(t)= # of {n| S_n .ltoreq t}, t .gtoreq 0, is a nonhomogeneous Poisson process.We characterize F by using some conditional expectations about {S_n, n .gtoreq 1}.