Benford Meets Nyquist

Benford s law implies the mantissa of all practical numbers should be distributed uniformly asmentioned by Necomb in his 1881 paper. One might think having a uniform mantissa for X isequivalent to a uniformly distributed logarithm for X when range of X is large enough as has beenstated by some sources. Uniform log, however, limits Benford s law to a handful of distributions only.The question then arises that why all practical numbers should follow this limited set of distributions More importantly, how can Ted Hill s proof of Benford as a distribution of all distributions be justifiedwhen only a handful of common distributions are really Benford-like In this paper we attempt toaddress this dilemma by first digging into the mantissa requirement. We then show how thisrequirement bridges statistics to the field of telecommunication.

Keywords:

Benford s law , Nyquist Inter-Symbol Interference Theorem , Mantissa , Statistics , Telecommunication