中文摘要：

变异系数是一项可靠性指标,它应用于既有结构的可靠性、医院统计及保险理论等方面,对变异系数进行假设检验具有现实意义。本文取自一般正态总体的子样,并利用样本均值X珔、样本标准差S和变异系数v=σμ的关系构造了一种含变异系数的抽样分布Z=v XS珔～z（v,n-1）,同时给出了该分布的密度函数fZ（z）=（n 2-1）n2-1πv22nΓ（n 2-1）∫＋∞0 yn-1 e-21[（n-1）y2＋（yvz2-/1n）2]dy。本文给出一种对变异系数的小样本假设检验方法,根据该抽样分布及原假设成立的条件下确定检验统计量Z=v0 XS珔,然后利用统计量构造一个使备择假设成立的小概率事件,由此得出拒绝域或拒绝条件。

英文摘要：

Coefficient of variation is a reliability index.It is widely used in evaluation of reliability of existing structure,hospital statistics,insurance theory and so on.Hypothesis testing of the coefficient of variation is realistic significance.The sample of normal distribution is extracted,according to the relationship between sample mean,sample standard deviation S and coefficient of variation v=σμ,the sample distribution of containing coefficient of variation Z=vS~z（v,n-1） was given in this paper,at the same time its density function fZ（z）=n-12n-12πv22nΓn-12∫＋∞0yn-1e-12（n-1）y2＋（yz-1）2v2/ndy is given.A way of hypothesis test of the coefficient of variation is established in small sample.Through using the sample distribution and null hypothesis,test statistics Z=v0S is determined.Then a small probability events what makes alternative hypothes right is constructed,using this statistics.Thus rejection regions or rejection conditions are given.