On the Trigonometric Relation between Tax Audit and Underreporting Rates

26 Pages Posted: 1 Oct 2010 Last revised: 18 Feb 2015

See all articles by Jack Manhire

Jack Manhire

Texas A&M University School of Innovation; Bush School of Government & Public Service

Date Written: January 15, 2015

Abstract

The probabilities associated with a tax return being audited or containing underreported tax are formulated here in a different way. This new formulation is mathematically equivalent to the traditional formulation; however, it reveals a trigonometric relationship between these probabilities that cannot be deduced from the familiar approach. Unconditioned probabilities associated with audits and underreporting are expressed as the square of the magnitudes of probability amplitude vectors. Conditioned probabilities are expressed as the square of trigonometric functions (cosine or sine) of the angle between probability amplitude vectors and the axes of two-dimensional coordinate systems. Although applications are not discussed, this new way of considering tax audit and underreporting rates will hopefully inspire others to find solutions to problems otherwise thought unsolvable.

Keywords: audit rates, tax, taxation, tax compliance, tax underreporting, tax noncompliance, tax evasion, probability theory, probability amplitude, tax administration, measure theory, set theory

JEL Classification: C63, H2, H20, H24, H26, H29, K10, K34

Suggested Citation

Manhire, Jack, On the Trigonometric Relation between Tax Audit and Underreporting Rates (January 15, 2015). Available at SSRN: https://ssrn.com/abstract=1680142 or http://dx.doi.org/10.2139/ssrn.1680142

Jack Manhire (Contact Author)

Texas A&M University School of Innovation

1249 TAMU
College Station, TX 77843-1249
United States

Bush School of Government & Public Service ( email )

4220 TAMU
College Station, TX 76845
United States

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