一种基于灰色距离测度的小样本数据区间估计方法

Approach of parameter estimation for small samples based on grey distance measure

针对小样本试验数据的概率分布特征有时无法确定,传统概率统计就无法提供相应的参数估计方法的问题。基于灰色关联理论,首先定义了基于试验数据之间的拓扑关系和距离关系的灰色距离测度,通过对灰色距离测度的灰色生成得到小样本数据的参数估计值,并给出了满足一定灰色置信度下的参数置信区间。继而讨论了概率参数估计与灰色参数估计之间的区别。最后利用计算机对小样本试验数据的参数估计进行了仿真举例,示例结果表明所提方法简单合理,能有效地解决小样本数据参数估计的有关问题。

The times of the test is limited in the electronic equipment test, so the data of the test is small samples. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use traditional probability theory to process parameter estimation for small samples. The definition of the grey distance measure is given and the approach of the parameter estimation for small samples based on grey distance measure is introduced. At last several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach is feasible and effective to the parameter estimation for small samples.