几何分布的两个统计特征

Two Statistical Characterization of Geometric Distributions

  • 摘要: 本文研究如何用次序统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\le n, 使X_(k)-X_(1)同\X_(1)=2\及\X_(1)=4\独立,则X_1服从几何分布.(2)若存在k,\;1<k\le n, 使X_(k)-X_(1)同\X_(1)=3\及\X_(1)=4\独立,则X_1服从几何分布.

     

    Abstract: We make a detailed study of using the order statistics to depict the geometric distribution. The following two conclusions have been demonstrated in the present paper. First, if there exists a k,\;1<k\le n, such that X_(k)-X_(1) is independent of the event \X_(1)=2\ and \X_(1)=4\, then X_1 is geometric. Second, if there exists a k,\;1<k\le n, such that X_(k)-X_(1) is independent of the event \X_(1)=3\ and \X_(1)=4\, then X_1 is geometric.

     

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