An Empirical Non-Parametric Likelihood Family of Data-Based Benford-Like Distributions

22 Pages Posted: 22 Aug 2006

See all articles by Marian Grendar

Marian Grendar

Bel University; Institute of Measurement Science, Slovak Academy of Sciences; Institute of Mathematics and CS, Bel Univesity & SAS

George Judge

University of California, Berkeley - Department of Agricultural & Resource Economics

Laura Schechter

University of Wisconsin at Madison - Agricultural and Applied Economics; University of Wisconsin at Madison - Economics

Date Written: November 20, 2006

Abstract

A mathematical expression known as Benford's law provides an example of an unexpected relationship among randomly selected first significant digits (FSD). Newcomb (1881), and later Benford (1938), conjectured that FSDs would exhibit a weakly monotonic distribution and proposed a frequency proportional to the logarithmic rule. Unfortunately, the Benford FSD function does not hold for a wide range of scale-invariant multiplicative data. To confront this problem we use information-theoretic methods to develop a data-based family of Benford-like exponential distributions that provide null hypotheses for testing purposes. Two data sets are used to illustrate the performance of generalized Benford-like distributions.

Keywords: Benford's law, first significant digit phenomenon, relative frequencies

JEL Classification: C10, C24

Suggested Citation

Grendar, Marian and Judge, George G. and Schechter, Laura, An Empirical Non-Parametric Likelihood Family of Data-Based Benford-Like Distributions (November 20, 2006). Available at SSRN: https://ssrn.com/abstract=925727 or http://dx.doi.org/10.2139/ssrn.925727

Marian Grendar

Bel University ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

Institute of Measurement Science, Slovak Academy of Sciences ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

Institute of Mathematics and CS, Bel Univesity & SAS ( email )

Tajovskeho 40
SK-974 01 Banska Bystrica
Slovakia

George G. Judge

University of California, Berkeley - Department of Agricultural & Resource Economics ( email )

207 Giannini Hall
University of California
Berkeley, CA 94720
United States

Laura Schechter (Contact Author)

University of Wisconsin at Madison - Agricultural and Applied Economics ( email )

427 Lorch St.
Madison, WI 53706-1503
United States

HOME PAGE: http://aae.wisc.edu/lschechter

University of Wisconsin at Madison - Economics ( email )

William H. Sewell Social Science Building
1180 Observatory Drive
Madison, WI 53706-1393
United States

HOME PAGE: http://aae.wisc.edu/lschechter

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
90
Abstract Views
723
rank
319,057
PlumX Metrics