## Proof that a Data Set that Conforms to Benford's Law is not Always Sum Invariant with Respect to the First Digits

**Authors:** Robert C. Hall

The summation test consists of adding all numbers that begin with a particular first digit 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) i.e. y = a exp(kt) but not necessarily true for other data sets that conform exactly to Benford'a law.

**Comments:** 20 Pages.

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### Submission history

[v1] 2018-11-18 11:45:11

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