Ubiquity of Benford's law and emergence of the reciprocal distribution
Abstract
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.
- Authors:
-
- 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)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- Contributing Org.:
- Harvard Univ., Cambridge, MA (United States)
- OSTI Identifier:
- 1321724
- Alternate Identifier(s):
- OSTI ID: 1345436
- Report Number(s):
- LA-UR-13-20486
Journal ID: ISSN 0375-9601
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics Letters. A
- Additional Journal Information:
- Journal Volume: 380; Journal Issue: 22-23; Journal ID: ISSN 0375-9601
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Benford/Reciprocal distribution; Information/Communication theory; Iteration theory
Citation Formats
Friar, James Lewis, Goldman, Terrance J., and Pérez-Mercader, J. Ubiquity of Benford's law and emergence of the reciprocal distribution. United States: N. p., 2016.
Web. doi:10.1016/j.physleta.2016.03.045.
Friar, James Lewis, Goldman, Terrance J., & Pérez-Mercader, J. Ubiquity of Benford's law and emergence of the reciprocal distribution. United States. https://doi.org/10.1016/j.physleta.2016.03.045
Friar, James Lewis, Goldman, Terrance J., and Pérez-Mercader, J. Thu .
"Ubiquity of Benford's law and emergence of the reciprocal distribution". United States. https://doi.org/10.1016/j.physleta.2016.03.045. https://www.osti.gov/servlets/purl/1321724.
@article{osti_1321724,
title = {Ubiquity of Benford's law and emergence of the reciprocal distribution},
author = {Friar, James Lewis and Goldman, Terrance J. and Pérez-Mercader, J.},
abstractNote = {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.},
doi = {10.1016/j.physleta.2016.03.045},
journal = {Physics Letters. A},
number = 22-23,
volume = 380,
place = {United States},
year = {Thu Apr 07 00:00:00 EDT 2016},
month = {Thu Apr 07 00:00:00 EDT 2016}
}
Web of Science
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