修正Benford分布律及其在数据准确性评估中的应用

发布时间：2018-02-16 15:42

本文关键词： 数据准确性修正Benford分布律加权平均　出处：《天津财经大学》2016年硕士论文　论文类型：学位论文

【摘要】：统计数据是统计决策的重要依据,其准确性直接影响着统计决策的正确性。统计数据已经被看作一种特殊的生产要素,准确的统计数据已经广泛应用于社会主义经济建设、民主和法制建设中。在此背景下,国内外学者研究了众多方法评估统计数据的准确性。其中Benford分布律是评估数据准确性的常用方法,被广泛用于会计、审计领域,宏观经济领域等多个领域的统计数据准确性评估。国内学者对Benford分布律统计性质方面的研究较少。适用于Benford分布律评估的数据需要满足一定的假设条件,这使得Benford分布律的应用存在一定的局限性。针对上述问题,在对国内外学者采用Benford分布律评估统计数据准确性的研究进行了梳理后,随机模拟比较了 Benford分布律与几种常见分布。并且,总结了 Benford分布律的局限性。针对Benford分布律不能用于有界数据集准确性评估的局限性,提出了修正Benford分布律。给出了修正Benford分布律的算法,以及用于数据准确性评估的方法,通过统计模拟分析,比较了修正Benford分布律与Benford分布律之间的差异,结果显示修正Benford分布律有较优良的统计性质,与传统的Benford分布律相比具有更好的适用性。并利用修正Benford分布律对367个县级城市的主要数据准确性进行了评估。
[Abstract]:Statistical data is an important basis for statistical decision-making, and its accuracy directly affects the correctness of statistical decision-making. Statistical data have been regarded as a special factor of production, and accurate statistical data have been widely used in socialist economic construction. In the construction of democracy and legal system, scholars at home and abroad have studied many methods to evaluate the accuracy of statistical data. Benford distribution law is widely used in the field of accounting and auditing. The accuracy evaluation of statistical data in many fields, such as macroeconomic field, is seldom studied by domestic scholars. The data suitable for Benford distribution law evaluation need to satisfy some assumptions. This makes the application of Benford distribution law have some limitations. In view of the above problems, after combing the domestic and foreign scholars using Benford distribution law to evaluate the accuracy of statistical data, The Benford distribution law and several common distributions are compared by random simulation, and the limitations of Benford distribution law are summarized. The limitation of Benford distribution law can not be used to evaluate the accuracy of bounded data set. In this paper, the modified Benford distribution law is proposed, the algorithm of the modified Benford distribution law and the method used to evaluate the accuracy of the data are given. The difference between the modified Benford distribution law and the Benford distribution law is compared by statistical simulation analysis. The results show that the modified Benford distribution law has better statistical properties and better applicability than the traditional Benford distribution law, and the accuracy of the main data in 367 county-level cities is evaluated by using the modified Benford distribution law.
【学位授予单位】：天津财经大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：C81

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