BenfordTests (version 0.5)

Freedman_Watson_Usquare_benford: Freedman-Watson U-squared Test for Benford's Law

Description

Freedman_Watson_Usquare_benford takes any numerical vector reduces the sample to the specified number of significant digits and performs the Freedman-Watson test for discreet distributions between the first digits' distribution and Benford's distribution to assert if the data conforms to Benford's law.

Usage

Freedman_Watson_Usquare_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 U-square test statistic
• p.value
  the p-value for the test
• method
  a character string indicating the type of test performed

Details

A Freedman-Watson test for discreet distributions is performed 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. Freedman LS. Watson's Un2 statistic for a discrete distribution. Biometrika. 1981;68(3):708-711. Watson GS. Goodness-of-fit tests on a circle. Biometrika. 1961;48:109-114.

See Also

pbenf