Modifications to the Jarque–Bera Test
Full article
| Journal |
Mathematics
, E-ISSN: 2227-7390
|
| Output data |
Year: 2024,
Volume: 12,
Article number
: 2523,
Pages count
: 16
DOI:
10.3390/math12162523
|
| Tags |
normality test; Jarque–Bera test; skewness; kurtosis; Monte Carlo simulation |
| Authors |
Glinskiy Vladimir
1,2
,
Ismayilova Yulia
1
,
Khrushchev Sergey
3
,
Logachov Artem
1,4
,
Logachova Olga
5
,
Serga Lyudmila
1,2
,
Yambartsev Anatoly
6
,
Zaykov Kirill
1
|
| Affiliations |
| 1 |
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
|
| 2 |
Department of Statistics, Novosibirsk State University of Economics and Management, 630099 Novosibirsk, Russia
|
| 3 |
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, 630090 Novosibirsk, Russia
|
| 4 |
Department of Computer Science in Economics, Novosibirsk State Technical University (NSTU), 630087 Novosibirsk, Russia
|
| 5 |
Department of Higher Mathematics, Siberian State University of Geosystems and Technologies (SSUGT), 630108 Novosibirsk, Russia
|
| 6 |
Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo (USP), São Paulo CEP 05508-220, Brazil
|
|
Funding (1)
|
1
|
Russian Science Foundation
|
24-28-01047
|
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 Citation: Glinskiy, V.; Ismayilova, Y.; Khrushchev, S.; Logachov, A.; Logachova, O.; Serga, L.; Yambartsev, A.; Zaykov, K. Modifications to the Jarque–Bera Test. Mathematics 2024, 12, 2523. https://doi.org/10.3390/ math12162523 Academic Editors: María del Carmen Valls Martínez and Davide Valenti Received: 20 June 2024 Revised: 29 July 2024 Accepted: 13 August 2024 Published: 15 August 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 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.