  The Newcomb-Benford probability distribution is becoming very popular in many
areas using statistics, notably in fraud detection. In such contexts, it is
important to be able to determine if a data set arises from this distribution
while controlling the risk of a Type 1 error, i.e. falsely identifying a fraud,
and a Type 2 error, i.e. not detecting that a fraud occurred. The statistical
tool to do this work is a goodness-of-fit test. For the Newcomb-Benford
distribution, the most popular such test is Pearson's chi-square test whose
power, related to the Type 2 error, is known to be weak. Consequently, other
tests have been recently introduced. The goal of the present work is to build
new goodness-of-fit tests for this distribution, based on the smooth test
principle. These tests are then compared to some of their competitors. It turns
out that the proposals of the paper are globally preferable to existing tests
and should be seriously considered in fraud detection contexts, among others.
