## 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.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 36 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*