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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������;�Ѻ���;���ػ�. ���ηֲ�������ͳ������[J]. Ӧ�ø���ͳ��, 2006, 22(1): 10-20.
XU XIAOLIN;FEI HELIANG;WANG RONGHUA. Two Statistical Characterization of Geometric Distributions. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2006, 22(1): 10-20.
