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Hill pointed out in his landmark paper that “An interesting open problem is to determine which common distributions (or mixtures thereof) satisfy Benford’s law …”. Ever-since, there has been many attempts in finding distributions that are precisely compliant with Benford’s law. Even though sufficient conditions were derived and some ad-hoc distributions were reported in the literature, the lack of a general framework for generating such distributions is sensed. Almost all of the reported Benford-compliant distributions are finite-length. This paper looks at the problem from an electrical engineer’s perspective; it harnesses the literature on Nyquist inter-symbol interference theorem and then proposes a framework for generating infinite-length or arbitrary long finite-length distributions satisfying Benford’s law.

A general framework for constructing distributions satisfying Benford’s law