The Probability Interpretation Of Benford's Law And Its Application In Finance

In the era of big data,Benford's Law,as a specail distribution of first significant digit,is increasly playing an important role in detecting fraud or monitoring abnormal behavior in data.The dissertation described some research results about the Law in theory and application.It contains five chapters:In the first chapter,the backgrounds of Benford's Law were introduced,including the motivation,the discovery of the Law,and the hostorical research.In the second chapter,some previous important mathematical results about Benford's Law were reviewed,focusing on probability interpretions based on several basic assumptions.In the third chapter,the question which common probability distribution is obeying Benford's Law was partly answered and the Log-normal?Weibull?Inverse Gamma distribution were selected to be studied.In the fourth chapter,China Stock Market was checked by Benford's law and some related questions were studied.In the final chapter,the main results were comprehensively concluded and some questions about the Law in theory and application were raised.Based on the previous research,several methods were adopted to prove that the three probability distributions:the Log-normal,the Weibull distribution and the Inverse Gamma distribution are close to Benford's Law when their parameters satisfy some conditions,which partly answeared Hill's question,which confirmed that Benford's Law is almost universal.China Stock Market was checked by Benford's Law and was verified to obey the law in natural state.It was confirmed when there was abnormal behavior there was deviation from the law happening,vice versa.Finally,the abnormal behavior could be explained by some interventions.The result can provide beneficial references for suervisors in China?...