Modifications to the Jarque–Bera Test

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)

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.

Glinskiy V. , Ismayilova Y. , Khrushchev S. , Logachov A. , Logachova O. , Serga L. , Yambartsev A. , Zaykov K.
Modifications to the Jarque–Bera Test
Mathematics. 2024. V.12. 2523 :1-16. DOI: 10.3390/math12162523 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 29, 2024
Accepted:	Aug 13, 2024
Published print:	Aug 15, 2024
Published online:	Aug 15, 2024

Web of science:	WOS:001305346900001
Scopus:	2-s2.0-85202584622
Elibrary:	74326396
OpenAlex:	W4401611833

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