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In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.
The test statistic JB is defined as
where n is the number of observations ; S is the sample skewness, K is the sample kurtosis :
where μ ^ 3 {\displaystyle {\hat {\mu }}_{3}} and μ ^ 4 {\displaystyle {\hat {\mu }}_{4}} are the estimates of third and fourth central moments, respectively, x ¯ {\displaystyle {\bar {x}}} is the sample mean, and σ ^ 2 {\displaystyle {\hat {\sigma }}^{2}} is the estimate of the second central moment, the variance.