An empirical non-parametric likelihood family of data-based Benford-like distributions
AbstractA mathematical expression known as Benford's law provides an example of an unexpected relationship among randomly selected sequences of first significant digits (FSDs). Newcomb [Note on the frequency of use of the different digits in natural numbers, Am. J. Math. 4 (1881) 39–40], and later Benford [The law of anomalous numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551–572], conjectured that FSDs would exhibit a weakly monotonic decreasing 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 alternative 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 380 (2007)
Issue (Month): C ()
Contact details of provider:
Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Benford's law; First significant digit phenomenon; Relative frequencies; Information-theoretic method; Empirical likelihood; Minimum-divergence distance measure;
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Lee, Joanne & Cho, Wendy K. Tam & Judge, George G, 2009. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9745m98d, Department of Agricultural & Resource Economics, UC Berkeley.
- Paul Hofmarcher & Kurt Hornik, 2013. "First Significant Digits and the Credit Derivative Market During the Financial Crisis," Contemporary Economics, University of Finance and Management in Warsaw, vol. 7(2), June.
- Lee, Joanne & Judge, George G, 2008. "Identifying falsified clinical data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8x00h1c1, Department of Agricultural & Resource Economics, UC Berkeley.
- Lee, Joanne & Cho, Wendy K. Tam & Judge, George G., 2010. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 82-88, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.