臺灣博碩士論文加值系統

本論文討論一些有關非齊性 Poisson 過程及記錄值的刻劃。在第一章,
設有一非齊性 Poisson 過程 {N(t), t .gtoreq 0}, 以 {S_n, n
.gtoreq 1} 表到達時刻的過程, .gamma_t 及 delta_t 分別表在時間 t
之剩餘壽命及現在壽命。我們給一些關於 {S_n,n .gtoreq 1},
.gamma_t 及 .delta_t 的性質使得 {N(t), t .gtoreq 0} 成為一齊性
Poisson 過程。在第二章,自一組獨立且有共同分佈之隨機變數,{X_n, n
.gtoreq 1} , 且以 F 為其共同之分佈函數, 定義出記錄值之數列{S_n,
n .gtoreq1}。我們知道 {N(t),t .gtoreq 0} 為一非齊性 Poisson 過
程, 其中 N(t) = # of {n| S_n .ltoreq t}, t .gtoreq 0。利用關於
{S_n, n .gtoreq 1} 的條件期望值, 我們刻劃 F。

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}.