我們知道記錄值及順序統計量兩者有密切的關係。當我們將記錄值及順序統計量皆視作點過程，則這兩個過程都擁有順序統計量性質。Beg and Balasubramanian(1990), Wu and Ouyang(1996), 及 Huang and Su(1999)等人關於記錄值及順序統計量的研究結果使我們想要更進一步研究關於順序統計量之條件期望值之更一般的刻劃。然而，在點過程中有很多關於齊性Poisson過程的刻劃皆基於指數分佈的無記憶性質。又由Asadi(1999)關於Gumble二變量指數分佈或二變量幾何分佈刻劃的研究結果，促使我們想要探討若對二變量不獨立的齊性Poisson過程是否也有類似的刻劃結果。

It is known that record values and order statistics are closely related. When record values and order statistics are viewed as point processes, the two processes both share the order statistics property. The results of Beg and Balasubramanian(1990), Wu and Ouyang(1996), and Huang and Su(1999) about record values and order statistics motivated us to investigate more general results of characterization for order statistics point processes by using conditional
expectations based on order statistics. On the other hand, in the class of point processes, there are a lot of characterizations of homogeneous Poisson processes based on the memoryless property of exponential distribution. The result of Asadi(1999) about characterization of the Gumble bivariate exponential or the bivariate geometric distribution inspired us be interested in investigating some similar results about non-independent bivarite homogeneous Poisson processes.

1. Introduction 1

2. Order statistics property 4

3. Characterizations based on

conditional expectations of order
statistics 5

4. The results of non-independent

bivariate homogeneous Poisson
processes 12

5. Discussion 15

References 17

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