二次型之比服从F-分布的充分必要条件(英文)  

The Necessary and Sufficient Conditions for the Ratios of Quadratic Forms to be Distributed as F-distributions

作　　者：秦怀振[1] 崔恒建[1] 李勇[1] 

机构地区：[1]北京师范大学,北京100875

出　　处：《应用概率统计》1998年第1期79-84,共6页Chinese Journal of Applied Probability and Statistics

摘　　要：考察F－分布的密度和矩，本文给出了正态随机向量二次型之比服从F－分布的充分必要条件，进而给出了椭球等高随机向量二次型之比服从F分布的充分必要条件．作为应用，我们减弱了传统F－检验中对两简单子样独立性的要求．　The necessary and sufficient conditions such that the ratios of quardratic forms in multinor-mal random vectors have F-distributions are obtained by investigating the density functions and　moments of F-distributions and moments of F-distributions. Furthermore, the necessary and　sufficient conditions for the ratios of quadratic forms contoured random vectors to be distributed　as F-distributions are also obtained. As applications, we extend the classical F-test to some　dependent two group samples.

关 键 词：多元正态分布 F-分布 F-检验 充要条件 二次型 

分 类 号：O212.1[理学—概率论与数理统计]