Jarque-Bera test

The Jarque-Bera test checks whether regression residuals are normally distributed by comparing their sample skewness and kurtosis to the values expected under normality, producing a statistic compared to a chi-square distribution.

ByHoang TruongUpdated July 5, 2026

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A regression's 100 residuals show a sample skewness of 0.3 and kurtosis of 3.6, close to the normal benchmarks of 0 and 3. The Jarque-Bera statistic, (100 ÷ 6) × [0.3² + 0.6² ÷ 4], works out to 3.00, comfortably below the 5.99 chi-square critical value, so there is no strong evidence against normality.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicRegression Diagnostics & ProblemsAdvanced

The formula

LaTeX

JB = \dfrac{n}{6}\left[S^2 + \dfrac{(K-3)^2}{4}\right]

Variables

$n$: Number of residuals
$S$: Sample skewness of the residuals
$K$: Sample kurtosis of the residuals

Tests whether residuals' skewness and kurtosis are consistent with a normal distribution; compared to a chi-square distribution with 2 degrees of freedom.