Modifications to the Jarque–Bera Test

Vladimir Glinskiy (), Yulia Ismayilova, Sergey Khrushchev, Artem Logachov, Olga Logachova, Lyudmila Serga, Anatoly Yambartsev and Kirill Zaykov
Additional contact information
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
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
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
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

Mathematics, 2024, vol. 12, issue 16, 1-16

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.

Keywords: normality test; Jarque–Bera test; skewness; kurtosis; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2523/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2523/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2523-:d:1457138

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().