Assessing Conformity to Benford’s Law with Application to Check China Financial Market

Abstract

Benford’s law states that the basic distribution of first digits in naturally produced data is that the frequency of first digits decreases as the digits become larger. This law has been widely used in many areas, such as detecting fraud or manipulation in large datasets. Goodness-of-fit tests are used to assess whether the data obeyed Benford’s law. However, conventional statistical tests reject the null hypothesis that data obey Benford’s law if the data size is very large. In this paper, we calculated the empirical distribution of first digits of stock close price and daily return in China Stock Market and assessed their conformity to Benford’s law by several statistical tests. As a comparison, we introduce the distribution of first two digits as another kind of Benford’s law and test whether China Stock Market is close to the law.