【作者】 王欣；

【导师】 杨贵军；

【作者基本信息】 天津财经大学 ， 统计学， 2016， 硕士

【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。更多还原

【Abstract】 As an important basis for the statistical decision,Statistical data’s accuracy directly affects the direction and the correctness of the statistical decision.At present,statistics data have been a special kind of factors of production,the accurate statistics have been widely applied to the development of market economy,democracy,legal construction and the harmonious society.In this context,many scholars have studied the method to evaluate the accuracy of statistical data,both at home and abroad.Benford’s Law is one of the commonly used methods to assess the accuracy of the data,and it’s widely used to evaluate the accuracy of statistical data in the field of accounting,auditing,macro economy,and so on.Domestic scholars pay little attention to the statistical property of Benford’s Law now.What’s more,because of there being some assumptions when using Benford’s Law to evaluate data,it makes the Benford’s Law has limitations in application.Aiming at an attentive solving of the problems above,this paper summarizes the researches about using Benford’s Law as a method to assess the accuracy of the statistics at home and abroad.Then,this paper compares the relationship between Benford’s Law and the common distribution by the method of stochastic simulation.In addition,it summarizes the limitations of Benford’s Law,and for improving assumption conditions of Benford’s Law,this paper proposes a new method called corrected Benford’s distribution.This paper gives the algorithm for generating the corrected Benford’s distribution,and through the statistical simulation analysis,compares the difference between the corrected Benford’s distribution and Benford’s distribution in the aspect of assessing the data accuracy.The simulation studies show that the new method is better than the Benford’s Law in aspect of assessing the data accuracy.Moreover,this paper also uses the new method to assess the accuracy of 13 indicators data of the 367 county-level cities in China.更多还原