| Summary: | 碩士 === 國立高雄大學 === 統計學研究所 === 96 === For k>= 1, let {R_n^{(k)},n>= 1} and {W_n^{(k)},n>=
1} be respectively kth record values and weak kth record
values from discrete distribution function F with support D.
Some properties and characterizations of {R_n^{(k)},n>= 1}
and {W_n^{(k)},n>= 1} will be studied. More precisely, first
for k=2, we will demonstrate that the distribution function F
can not be characterized by the condition
E(R_1^{(k)}-R_0^{(k)}|R_0^{(k)}=y)=c, y in D, where
c>=2^(1/2) is a constant. Next, under some extra conditions,
the characterizations based on the condition
E(R_1^{(k)}-R_0^{(k)}|R_0^{(k)}=y)=c, y in D, will be studied.
Also we will give some characterizations based on the joint
distributions of (R_0^{(k)},R_1^{(k)},...,R_n^{(k)}) and
(W_0^{(k)},W_1^{(k)},...,W_n^{(k)}). Finally considering the
support D=\{0,1,...,N\}, where N<infty, we will show that
for n>= 0, the distribution function F can be uniquely
determined by conditional expectations
g(y)=E(phi(W_{n+2}^{(1)})|W_n^{(1)}=y), y in D, where phi
is a strictly monotone function.
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