Grey confidence interval estimation of small samples based on numerical characteristics

For the problem of small samples estimation in engineering practice, a new method of the grey confidence interval estimation for small samples based on numerical characteristics is studied. According to the degree of aggregation of small sample data, the concept of the distance standard deviation, which is an important numerical characteristic, is defined. At the same time, the concept of sample dispersion degree is proposed to describe the degree of dispersion between different samples. On the basis of the new definition of grey weight, the grey point estimation is proposed. Then, the grey distance approach improved by distance standard deviation and sample distance, are put forward with their numerical characteristic. In addition, the accurate grey bilateral and unilateral confidence intervals are introduced under the new grey distance approach. Finally, several examples are used to demonstrate the rationality and effectiveness of the methods proposed above. The comparative results show that the proposed methods have higher precision in reflecting the characteristics of data density.