Jarque-Bera Test

Jarque-Bera test is a normality test that combines sample skewness and excess kurtosis into one chi-square statistic with two degrees of freedom, rejecting normality when either departs from zero.

자크-베라 검정은 표본의 왜도와 초과첨도를 자유도 2인 카이제곱 통계량 하나로 묶어, 둘 중 하나라도 0에서 벗어나면 정규성을 기각하는 정규성 검정이다.

How do I check whether the skewness and kurtosis of my data are consistent with a normal distribution?

데이터의 왜도와 첨도가 정규분포와 맞는지 어떻게 검정하나요?

The Jarque-Bera test asks whether the sample skewness and kurtosis jointly match those of a normal distribution, using a statistic that follows a chi-square distribution with two degrees of freedom in large samples. It is common for regression residuals and financial returns, but its asymptotic p-value is unreliable in small samples.

When to use Jarque-Bera Test

• Large samples, such as economic or financial series, where normality is to be checked
• Checking regression residuals for skewness or excess kurtosis
• Reporting skewness and kurtosis together with one formal test

When to use something else

• Samples under about 50 observations: use the Shapiro-Wilk test
• Checking fit to a fully specified non-normal distribution: use the Kolmogorov-Smirnov test

Assumptions and requirements

• Independent observations
• Continuous variable
• Large sample, since the chi-square reference distribution is asymptotic

What the analysis reports

• JB statistic
• p-value from the chi-square distribution with 2 degrees of freedom
• Sample skewness
• Excess kurtosis (0 for a normal distribution)
• Warning when the sample has fewer than 50 observations

How to report it

A Jarque-Bera test indicated that [variable] departed significantly from normality, JB = [value], p = [value] (skewness = [value], excess kurtosis = [value]).

Related methods

• Shapiro-Wilk Test
• Anderson-Darling Test
• Kolmogorov-Smirnov Test

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