## Comparison of the Theoretical and Empirical Results for the Benford's Law Summation Test Performed on Data that Conforms to a Log Normal Distribution

**Authors:** Robert C. Hall

The Benford's Law Summation test consists of adding all numbers that begin with a particular first or first two digits and determining its distribution with respect to these first or first two digits numbers. Most people familiar with this test believe that the distribution is a uniform distribution for any distribution that conforms to Benford's law i.e. the distribution of the mantissas of the logarithm of the data set is uniform U[0,1). The summation test that results in a uniform distribution is true for an exponential function (geometric progression) but not true for a data set that conforms to a Log Normal distribution even when the Log Normal distribution itself closely approximates a Benford's Law distribution.

**Comments:** 24 Pages.

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### Submission history

[v1] 2019-01-03 17:17:16

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