统计量服从特定分布的充要条件

当正态总体的方差未知时，人们常用t检验法来检验总体的均值．事实上，这种检验方法并不一定要求总体是正态分布，甚至样本之间的独立性要求也不是必要的．本文的目的是研究t检验的适用范围，给出了二维随机向量构成服从t分布统计量的充要条件．出于类似的目的，还给出了二维随机向量构成服从Dirichlet分布及F分布统计量的充要条件．

The sufficient and necessary conditions for a test statistic submitting to certain distribution

When the variance of a normal population is unknown, as to the test of mean for the population, we usually use t test. In fact, this method of test does not require that the poulation is normal distribution; even the independence among the samples is unnecessary. The purpose of this paper is to find the applying region of the t test, i.e. the necessary and sufficient conditions for a two dimension variable forms a test, which possesses a t distribution. As to the similar purpose, we also give the necessary and sufficient conditions for two tests, one has a Dirichlet distribution, and the other has a F distribution respect.