Summary: | 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}.
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