V.M. Artyushenko1, V.I. Volovach2

1 Moscow State University of Geodesy and Cartography (Moscow, Russia)

2 Volga Region State University of Service (Toglyatti, Russia) 2 MIREA – Russian Technological University (Moscow, Russia)

1 artuschenko@mail.ru, 2, 3 volovach.vi@mail.ru

The paper discusses the problem of checking the homogeneity of two samples by variances under conditions of deviation of distributions from normality. It is noted that the classic F-test has a high sensitivity to data abnormality and can give unreliable results. The existing robust approaches are analyzed and their limitations related to the requirement of knowledge of mathematical expectations and the impossibility of applying with different excesses of distributions is discussed. Based on the above approximation considerations, the article proposed and analyzed a new robust F-criterion that retains performance for samples extracted from distributions with pro-arbitrary, including different, excesses.

The purpose of this study is to construct a robust F-test that allows checking the consistency of the variances of two samples in the general case, that is, without assumptions about the equality of excesses, as well as to develop a practical procedure for its application.

A practical procedure for applying a new robust F-test has been developed and a comparative experiment has been conducted, the results of which demonstrate its advantages over standard methods. Two statistical procedures were considered for applying a robust F-test of equality of variances for two samples from distributions with any excesses – using a selective estimate and an exact excess value. A practical approximate expression for kurtosis is obtained.

The results obtained confirm the effectiveness and practical significance of the new robust F-test, including the case of the absence of assumptions about the equality of excesses. At the same time, the proposed solutions allow the use of an approximate expression convenient for practice for kurtosis.

Artyushenko V.M., Volovach V.I. Mathematical algorithms for checking homogeneity with respect t o the variances of two nonGaussian samples. Nonlinear World. 2026. V. 24. № 1. P. 23–35. DOI: https:// doi.org/10.18127/ j20700970-202601-02 (In Russian)

1. Mardia K., Zemroch P. Tablicy F-raspredeleniya iraspredelenij, svyazannyh s nim. M.: Nauka. 1984. 255 s. (In Russian).
2. Rytov S.M. Vvedenie vstatisticheskuyu radiofiziku. Ch.1. M.: Nauka. 1976. 494 s. (In Russian).
3. Sheffe G. Dispersionnyj analiz. M.: Nauka. 1980. 512 s. (In Russian).
4. Ahmanov S.A., D'yakov Yu.E., Chirkin A.S. Statisticheskaya radiofizika ioptika. Sluchajnye kolebaniya ivolny vlinejnyh sistemah. Izd. 2-e, pererab. i dop. M.: Fizmatlit. 2010. 425 s. (In Russian).
5. Ivanov A.A., Leonenko N. Statistical analysis of randomfields. Springer Science & Business Media, 2012. 244 p.
6. Tonggumnead U., Saengngam N. DevelopmentoftheRobustTestforTestingtheHomogeneityof Variances and Its Applications. WSEAS Transactions on Mathematics. 2025. V. 24. P. 90–113. https://doi.org/10.37394/23206.2025.24.12.
7. Adeniran A.T., Olilima J.O., Akano R.O. Analysis of variance: The fundamental concepts and application with R. International Journal of Multidisciplinary and Current Research. 2021. V.
8. Is. 10. P. 2408–2422. DOI: https://doi.org/10.47191/ijmcr/v9i10.04.
9. Mohseni N., Bernstein D.S. Recursive leastsquares with variable-rateforgetting based on the F-test. 2022 American Control Conference (ACC). IEEE. 2022. P. 3937–3942. DOI: https://doi.org/10.23919/ACC53348.2022.9867849.
10. Blanchette K., Burr W., Takahara G. An F-test for polynomial frequency modulation. 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. 2021. P. 5010–5014. DOI: https://doi.org/10.1109/ICASSP39728.2021.9414209. 1
11. Mozhaeva T., Gorlenko O., Borbac' N. Dispersionnyj analiz eksperimental'nyh dannyh: Uchebnik dlyavuzov. Izd. 2-e, ispr. i dop. M.: Yurajt. 2025. 132 s. (In Russian) 1
12. Orlov A.I. O metodahproverki odnorodnosti dvuhnezavisimyh vyborok. Zavod skayalaboratoriya. Diagnostika materialov. 2020. T. 86. № 3. S. 67–75. DOI: https://doi.org/10.26896/1028-6861-2020-86-3-67-76 (In Russian). 1
13. Krivosheev I.A., Ivanov G.A. Robastnyj metodobrabotki eksperimental'nyh dannyh. Defektoskopiya. 2003. № 8. S. 35–40 (In Russian). 1
14. Shulenin V.P. Vvedenie vrobastnuyu statistiku. Tomsk: Izd-vo Tomskogo un-ta. 1993. 227 s. (In Russian) 1
15. Artyushenko V.M., Volovach V.I. Formation of non-Gaussian randomprocesses, signals and noise based on stochastic differential equations. Part
16. Nelinejnyj mir. 2019. T. 17. № 2. S. 64–71. DOI: https://doi.org/10.18127/j20700970-201902-08. 1
17. Artyushenko V.M., Volovach V.I. Formation of non-Gaussian randomprocesses, signals and noise based on stochastic differential equations. Part
18. Nelinejnyj mir. 2019. T. 17. № 3. S. 45–51. DOI: https://doi.org/10.18127/j20700970-201903-05. 1
19. Montgomeri D.K. Planirovanie eksperimenta ianaliz dannyh. L.: Sudostroenie. 1980. 383 s. (In Russian) 1
20. Bol'shev L.N., Smirnov N.V. Tablicy matematicheskoj statistiki. M.: Nauka. 1983. 416 s. (In Russian) 1
21. Ahmanov S.A., D'yakov Yu.E., Chirkin A.S. Vvedenievstatisticheskuyuradiofizikuioptiku: Ucheb. poso bi edlyavuzov. M.: Nauka. 1981. 650 s. (In Russian) 1
22. Uilks S. Matematicheskaya statistika. M.: Nauka. 1967. 632 s. (In Russian) 2
23. Ivanov G.A., Ponomarchuk Yu.V., Chashkin Yu.R. Robastnyj kriterijproverki odnorodnosti dvuh negaussovskih vyborokotnositel'no dispersij. Izmeritel'nayatekhnika. 2005. № 2. S. 9–12 (In Russian). 2
24. Malahov A.N. Kumulyantnyj analizsluchajnyh negaussovskih processov i ih preobrazovanij. M.: Sov. radio. 1978. 376 s. (In Russian)