Ubiquity of Benfords law and emergence of the reciprocal distribution

Autor:	Friar, J. L., Goldman, T., Perez-Mercader, J.
Rok vydání:	2016
Předmět:	Physics - Data Analysis Statistics and Probability Statistics - Other Statistics
Zdroj:	Physics Letters A 380, 1895 (2016)
Druh dokumentu:	Working Paper
DOI:	10.1016/j.physleta.2016.03.045
Popis:	We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), 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) pdfs results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. We separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropy for size-class distributions with uniform bin sizes. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1604.07391 Zobrazit plný text záznamu View this record from Arxiv