Modifications to the Jarque–Bera Test

Autor: Vladimir Glinskiy, Yulia Ismayilova, Sergey Khrushchev, Artem Logachov, Olga Logachova, Lyudmila Serga, Anatoly Yambartsev, Kirill Zaykov
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Mathematics, Vol 12, Iss 16, p 2523 (2024)
Druh dokumentu: article
ISSN: 12162523
2227-7390
DOI: 10.3390/math12162523
Popis: 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.
Databáze: Directory of Open Access Journals
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