The Newcomb-Benford law in its relation to some common distributions.

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many da...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Anton K Formann
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2010
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/41a392cd110f440095d8be810ed5d206
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:41a392cd110f440095d8be810ed5d206
record_format	dspace
spelling	oai:doaj.org-article:41a392cd110f440095d8be810ed5d2062021-12-02T20:21:50ZThe Newcomb-Benford law in its relation to some common distributions.1932-620310.1371/journal.pone.0010541https://doaj.org/article/41a392cd110f440095d8be810ed5d2062010-05-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/20479878/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors.Anton K FormannPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 5, Iss 5, p e10541 (2010)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Anton K Formann The Newcomb-Benford law in its relation to some common distributions.
description	An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors.
format	article
author	Anton K Formann
author_facet	Anton K Formann
author_sort	Anton K Formann
title	The Newcomb-Benford law in its relation to some common distributions.
title_short	The Newcomb-Benford law in its relation to some common distributions.
title_full	The Newcomb-Benford law in its relation to some common distributions.
title_fullStr	The Newcomb-Benford law in its relation to some common distributions.
title_full_unstemmed	The Newcomb-Benford law in its relation to some common distributions.
title_sort	newcomb-benford law in its relation to some common distributions.
publisher	Public Library of Science (PLoS)
publishDate	2010
url	https://doaj.org/article/41a392cd110f440095d8be810ed5d206
work_keys_str_mv	AT antonkformann thenewcombbenfordlawinitsrelationtosomecommondistributions AT antonkformann newcombbenfordlawinitsrelationtosomecommondistributions
_version_	1718374102484385792

The Newcomb-Benford law in its relation to some common distributions.

Ejemplares similares