25: BENFORD'S LAW: A COLLECTION OF FORMAL GOODNESS--OF--FIT TESTS BASED ON EMPIRICAL TRANSFORMS

Music City Center 

We propose a number of goodness--of--fit tests for the probability law of significant digits postulated by the celebrated Benford law. First, the observations are transformed either to uniformity, or to normality, or to exponentiality, or to the Poisson law. Then test statistics are formulated by means of L2--type contrasts between the empirical transform of the transformed data and the corresponding population quantity under the null hypothesis. We also address the problem of a relaxed null hypothesis that only accounts for the probability distribution of a given number of significant digits under Benford's law. Computational formulae are provided for each case, and the suggested tests are compared via a detailed Monte Carlo study that includes competitors as well popular alternatives to Benford's law. The methods are also applied on a few real--data sets

Empirical characteristic function

Empirical Laplace transform

Monte Carlo 

Section on Statistical Computing