| 摘要註: |
對 k>=1，令 {R_n^(k),n>=0} 和 {W_n^(k),n>=0} 分別表示由具support D 之離散分佈函數 F 所生成的k-記錄值與弱k-記錄值，在本論文中，我們將研究這些離散記錄值的分佈性質及其刻劃問題。首先，當k=2 時，我們證明，滿足條件E(R_1^(k)-R_0^(k)|R_0^(k)=y)=c,y in D，其中 c 為一常數，並無法像弱 k-記錄值一樣刻劃出分佈函數 F 為幾何。其次，我們探討當加入某些條件下，經由條件E(R_1^(k)-R_0^(k)|R_0^(k)=y)=c,y in D所得到之刻劃結果。此外，我們也給出一些與E(R_0^(k),R_1^(k),...,R_n^(k)) 以及(W_0^(k),W_1^(k),...,W_n^(k))聯合分佈函數相關的分佈刻劃定理。最後，當D={0,1,...,N}$，其中 N< infty，我們證明對一嚴格單調函數phi，分佈函數 F 可由條件期望值g(y)=E(phi(W_{n+2}^{(1)})|W_n^{(1)}=y),y\in D，唯一決定。 For k>= 1, let {R_n^{(k)},n>= 1} and {W_n^{(k)},n>=1} be respectively kth record values and weak kth recordvalues 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, firstfor k=2, we will demonstrate that the distribution function Fcan not be characterized by the conditionE(R_1^{(k)}-R_0^{(k)}|R_0^{(k)}=y)=c, y in D, wherec>=2^(1/2) is a constant. Next, under some extra conditions,the characterizations based on the conditionE(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 jointdistributions of (R_0^{(k)},R_1^{(k)},...,R_n^{(k)}) and(W_0^{(k)},W_1^{(k)},...,W_n^{(k)}). Finally considering thesupport D=\{0,1,...,N\}, where N= 0, the distribution function F can be uniquelydetermined by conditional expectationsg(y)=E(phi(W_{n+2}^{(1)})|W_n^{(1)}=y), y in D, where phiis a strictly monotone function. |