| Data processing of small samples based on grey distance information approach |
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| 作者单位： | Ke Hongfa（Coll.of Electronic Science and Engineering, National Univ. of Defense Technology, Changsha 410073, P. R. China;Unit 63880, Luoyang 471003, P. R. China） ;
Chen Yongguang（Coll.of Electronic Science and Engineering, National Univ. of Defense Technology, Changsha 410073, P. R. China;Unit 63880, Luoyang 471003, P. R. China） ;
Liu Yi（Coll.of Electronic Science and Engineering, National Univ. of Defense Technology, Changsha 410073, P. R. China;Unit 63880, Luoyang 471003, P. R. China） ; |
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| 摘 要： | Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of uncertainty. Using the grey relational theory and the norm theory, the grey distance information approach, which is based on the grey distance information quantity of a sample and the average grey distance information quantity of the samples, is proposed in this article. The definitions of the grey distance information quantity of a sample and the average grey distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed. Moreover, the information whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective.
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| 收稿时间： | 5 January 2006. |
Data processing of small samples based on grey distance information approach |
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| Authors: | Ke Hongfa Chen Yongguang Liu Yi |
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| Institution: | Coll.of Electronic Science and Engineering, National Univ. of Defense Technology, Changsha 410073, P. R. China;Unit 63880, Luoyang 471003, P. R. China |
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| Abstract: | Data processing of small samples is an important and valuable research problem in the electronic equipment test. Because it is difficult and complex to determine the probability distribution of small samples, it is difficult to use the traditional probability theory to process the samples and assess the degree of uncertainty. Using the grey relational theory and the norm theory, the grey distance information approach, which is based on the grey distance information quantity of a sample and the average grey distance information quantity of the samples, is proposed in this article. The definitions of the grey distance information quantity of a sample and the average grey distance information quantity of the samples, with their characteristics and algorithms, are introduced. The correlative problems, including the algorithm of estimated value, the standard deviation, and the acceptance and rejection criteria of the samples and estimated results, are also proposed. Moreover, the information whitening ratio is introduced to select the weight algorithm and to compare the different samples. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective. |
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| Keywords: | Data processing Grey theory Norm theory Small samples Uncertainty assessment Grey distance measure Information whitening ratio |
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