BenfordTests (version 0.5)

Chebyshev_dist_benford: Chebyshev Distance Test for Benford's Law

Description

Chebyshev_dist_benford takes any numerical vector reduces the sample to the specified number of significant digits and performs a goodness-of-fit test based on the Chebyshev distance between the first digits' distribution and Benford's distribution to assert if the data conforms to Benford's law.

Usage

Chebyshev_dist_benford(x = NULL, first_digits = 1, pvalmethod = "simulate", pvalsims = 10000)

Arguments

x

A numeric vector.

first_digits

An integer determining the number of first digits to use for testing, i.e. 1 for only the first, 2 for the first two etc.

pvalmethod

Method used for calculating the p-value. Currently only "simulate" is available.

pvalsims

An integer specifying the number of replicates used if pvalmethod = "simulate".

Value

• A list with class "code{htest}" containing the following components:
• statistic
  the value of the Chebyshev distance test statistic
• p.value
  the p-value for the test
• method
  a character string indicating the type of test performed

Details

A statistical test is performed utilizing the Chebyshev distance between leading_digits(x,first_digits) and pbenf(first_digits). x is a numeric vector of arbitrary length. Values of x should be continuous, as dictated by theory, but may also be integers. first_digits should be chosen so that leading_digits(x,first_digits) is not influenced by previous rounding.

References

Benford F. The law of anomalous numbers. Proceedings of the American Philosophical Society. 1938;78:551-572. Leemis LM, Schmeiser BW, Evans DL. Survival distributions satisfying Benford's law. The American Statistician. 2000;54(4):236-241. Morrow J. Benford's law, families of distributions and a test basis. 2010. http://www.johnmorrow.info/projects/benford/benfordMain.pdf.

See Also

pbenf