Resumen de TestingBenford’slaw:fromsmalltoverylargedata sets

Leonardo Campanelli

• We discuss some limitations of the use of generic tests, such as the Pearson’s χ2, for testing Benford’s law. Statistics with known distribution and constructed under the specific null hypothesis that Benford’s law holds, such as the Euclidean distance, are more appropriate when assessing the goodness-of-fit to Benford’s law, and should be preferred over generic tests in quantitative analyses. The rule of thumb proposed by Goodman for compliance checking to Benford’s law, instead, is shown to be statistically unfounded. For very large sample sizes (N > 1000), all existing statistical tests are inappropriate for testing Benford’s law due to its empirical nature. We propose a new statistic whose sample values are asymptotically independent on the sample size making it a natural candidate for testing Benford’s law in very large data sets.