对几何分布的统计特征的研究

Two Statistical Characterization of Geometric Distributions

研究用次序计量来刻划几何分布,证明了如下两个命题(:1)若存在k,1 <k ≤n,使X(k) -X(1)同{X(1)=3}及{X(1) =4}独立,则1服从几何分布;(2)若存在k,1 <k ≤n使X(k)-X(1)同{X(1) =3}及{X(1)=4}独立,则1服从几何分布。

We make a detailed study of using the order statistics to depict the geometric distribution.The fol-lowing two conclusions have been demonstrated in the present paper.First,if there exists k,1 <k ≤n,such that X(K)-X(1) is independent of the event { X(1)1 = 2} and { X(1) 1 = 4},then X1 is geometric.Second,if there exists a k,1 <k ≤n such that X(k) -X(1) is independent of the event { X(1) =3} and{ X(1)=4},then is geometric.