Ubiquity of Benford's law and emergence of the reciprocal distribution
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
- Harvard Univ., Cambridge, MA (United States). Dept. of Earth and Planetary Sciences; Santa Fe Inst. (SFI), Santa Fe, NM (United States)
In this paper, we apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdf's), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdf's results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. Finally, we separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropy for size-class distributions with uniform bin sizes.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Contributing Organization:
- Harvard Univ., Cambridge, MA (United States)
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1321724
- Alternate ID(s):
- OSTI ID: 1345436
- Report Number(s):
- LA-UR-13-20486
- Journal Information:
- Physics Letters. A, Vol. 380, Issue 22-23; ISSN 0375-9601
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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