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Modifications to the Jarque–Bera Test

Author

Listed:
  • Vladimir Glinskiy

    (Department of Business Analytics, Accounting and Statistics and Research Laboratory of Sustainable Development of Socio-Economic Systems, Siberian Institute of Management—Branch of the Russian Presidential Academy of National Economy and Public Administration, 630102 Novosibirsk, Russia
    Department of Statistics, Novosibirsk State University of Economics and Management, 630099 Novosibirsk, Russia)

  • Yulia Ismayilova

    (Department of Business Analytics, Accounting and Statistics and Research Laboratory of Sustainable Development of Socio-Economic Systems, Siberian Institute of Management—Branch of the Russian Presidential Academy of National Economy and Public Administration, 630102 Novosibirsk, Russia)

  • Sergey Khrushchev

    (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, 630090 Novosibirsk, Russia)

  • Artem Logachov

    (Department of Business Analytics, Accounting and Statistics and Research Laboratory of Sustainable Development of Socio-Economic Systems, Siberian Institute of Management—Branch of the Russian Presidential Academy of National Economy and Public Administration, 630102 Novosibirsk, Russia
    Department of Computer Science in Economics, Novosibirsk State Technical University (NSTU), 630087 Novosibirsk, Russia)

  • Olga Logachova

    (Department of Higher Mathematics, Siberian State University of Geosystems and Technologies (SSUGT), 630108 Novosibirsk, Russia)

  • Lyudmila Serga

    (Department of Business Analytics, Accounting and Statistics and Research Laboratory of Sustainable Development of Socio-Economic Systems, Siberian Institute of Management—Branch of the Russian Presidential Academy of National Economy and Public Administration, 630102 Novosibirsk, Russia
    Department of Statistics, Novosibirsk State University of Economics and Management, 630099 Novosibirsk, Russia)

  • Anatoly Yambartsev

    (Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo (USP), São Paulo CEP 05508-220, Brazil)

  • Kirill Zaykov

    (Department of Business Analytics, Accounting and Statistics and Research Laboratory of Sustainable Development of Socio-Economic Systems, Siberian Institute of Management—Branch of the Russian Presidential Academy of National Economy and Public Administration, 630102 Novosibirsk, Russia)

Abstract

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, α = 0.05 and α = 0.01 , we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes n = 25 , 50 , 75 , 100 , 150 , 200 , 250 , 500 , and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera.

Suggested Citation

  • Vladimir Glinskiy & Yulia Ismayilova & Sergey Khrushchev & Artem Logachov & Olga Logachova & Lyudmila Serga & Anatoly Yambartsev & Kirill Zaykov, 2024. "Modifications to the Jarque–Bera Test," Mathematics, MDPI, vol. 12(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2523-:d:1457138
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    References listed on IDEAS

    as
    1. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    2. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
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