On the Kuiper Test for Benford’s Law

Name: On the Kuiper Test for Benford’s Law
Brand: Vita e Pensiero
Availability: OnlineOnly

digital

Article

Magazine

STATISTICA & APPLICAZIONI

Issue

STATISTICA & APPLICAZIONI - 2022 - 2

Title

On the Kuiper Test for Benford’s Law

Author

Leonardo Campanelli

Publisher

Vita e Pensiero

Format

Article |

Pdf

Pages

Online from

05-2025

Doi

10.26350/999999_000054

Issn

1824-6672 (print) | 2283-6659 (digital)

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Description Readers' comments

We show that the standard Kuiper test is inappropriate when testing Benford’s law. The Kuiper cumulative distribution function, indeed, shows unreasonable large deviations, up to about 60%, from the ones observed in Monte Carlo simulations. These deviations are scaled down to a level below 0:3% for moderately large and large numbers of data points (n 100) if an appropriate linear transformation of the argument of the Kuiper cumulative function is performed. The test based on the transformed Kuiper function is then accurate at a level of 1% when testing Benford’s law in data.

On the Kuiper Test for Benford’s Law by Leonardo Campanelli is licensed under CC BY-NC-ND 4.0

keywords

Kuiper Test, Benford’s law, Mathematical Modelling

Author biography

Department of Medicine - All Saints University School of Medicine - 5145 Steeles Ave. - M9L 1R5 - Toronto (ON), Canada (e-mail: leonardo.s.campanelli@gmail.com).

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