XU XIAOLIN, FEI HELIANG, WANG RONGHUA. Two Statistical Characterization of Geometric Distributions[J]. Chinese Journal of Applied Probability and Statistics, 2006, 22(1): 10-20.
Citation: XU XIAOLIN, FEI HELIANG, WANG RONGHUA. Two Statistical Characterization of Geometric Distributions[J]. Chinese Journal of Applied Probability and Statistics, 2006, 22(1): 10-20.
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Two Statistical Characterization of Geometric Distributions

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  • 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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