New upper bounds for noncentral chi-square cdf

Authors

  • Valeriy A. Voloshko Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Egor V. Vecherko Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Keywords:

noncentral chi-square distribution, upper bound

Abstract

Some new upper bounds for noncentral chi-square cumulative density function are derived from the basic symmetries of the multidimensional standard Gaussian distribution: unitary invariance, components independence in both polar and Cartesian coordinate systems. The proposed new bounds have analytically simple form compared to analogues available in the literature: they are based on combination of exponents, direct and inverse trigonometric functions, including hyperbolic ones, and the cdf of the one dimensional standard Gaussian law. These new bounds may be useful both in theory and in applications: for proving inequalities related to noncentral chi-square cumulative density function, and for bounding powers of Pearson’s chi-squared tests.

Author Biographies

  • Valeriy A. Voloshko, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); senior researcher at the laboratory of mathematical methods of information security

  • Egor V. Vecherko, Research Institute for Applied Problems of Mathematics and Informatics, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics), docent; head of the laboratory of mathematical methods of information security

References

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  4. Cook JD. Upper bounds on non-central chi-squared tails and truncated normal moments. UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series [Internet]. 2010 [cited 2020 January 11];62. Available from: https://www.johndcook.com/non_central_chi_square.pdf.

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Published

2020-03-31

Issue

No. 1 (2020): Journal of the Belarusian State University. Mathematics and Informatics

Section

Short Communications

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How to Cite

[1]
Voloshko, .V.A. and Vecherko, E.V. 2020. New upper bounds for noncentral chi-square cdf. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Mar. 2020), 70–74. DOI:https://doi.org/10.33581/2520-6508-2020-1-70-74.