The Sample Distribution and Hypothesis Test of Coefficient of Variation

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 X, sample standard deviation S and coefficient of variation *, the sample distribution of containing coefficient of variation * was given in this paper, at the same time its density function* dy 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 * 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.(* Indicates a formula, please see the full text)