Several researchers have observed that, in a wide variety of collections of numerical data, the leading — or most significant — decimal digits are not uniformly distributed, but conform to a logarithmic distribution. Of the nine possible values, occurs more than of the time while is found in less than of cases (see Figure above). Specifically, the probability distribution is

A more complete form of the law gives the probabilities for the second and subsequent digits. A full discussion of Benford’s Law is given in Berger and Hill (2015).