# Benford’s Law and Sum Invariance Testing

• Zoran Jasak
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 59)

## Abstract

Benford’s law is logarithmic law for distribution of leading digits formulated by P[D = d] = log(1 + 1/d) where d is leading digit or group of digits. It’s named by Frank Albert Benford (1938) who formulated mathematical model of this probability. Before him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number. One of main characteristic properties of this law is sum invariance. Sum invariance means that sums of significand are the same for any leading digit or group of digits. Term ‘significand’ is used instead of term ‘mantissa’ to avoid terminological confusion with logarithmic mantissa.

## Notes

### Acknowledgments

I wish to thank to Mr. Wilhelm Schappacher for great support in my work.

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