On the asymptotic power of the “energy” test for equality of two distributions

Authors

  • Vyacheslav B. Melas St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Dmitrii I. Salnikov St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2024.304

Abstract

In the paper the asymptotic distribution and the formula for the asymptotic power are found for the "energy" test in the case of alternative distributions differ from zero distribution by the parameter of shift and/or the parameter of scale. This criterion is an alternative for the well-known Mann-Whitney test but allows to compare distributions that differ by the scale parameter. The efficiency of the results obtained is demonstrated by the stochastic simulation for the normal distribution and the Cauchy distribution.

Keywords:

testing hypothesis of equality of two distributions, energy test, the asymptotic power of criteria, Normal distribution, Cauchy distribution

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Published

2024-10-15

How to Cite

Melas, V. B., & Salnikov, D. I. (2024). On the asymptotic power of the “energy” test for equality of two distributions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(3), 477–488. https://doi.org/10.21638/spbu01.2024.304

Issue

Vol. 11 No. 3 (2024)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.