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Jarque-Bera test

`h = jbtest(x)`

`h = jbtest(x,alpha)`

`h = jbtest(x,alpha,mctol)`

```
[h,p] =
jbtest(___)
```

```
[h,p,jbstat,critval]
= jbtest(___)
```

returns
a test decision for the null hypothesis that the data in vector `h`

= jbtest(`x`

)`x`

comes
from a normal distribution with an unknown mean and variance, using
the Jarque-Bera test.
The alternative hypothesis is that it does not come from such a distribution.
The result `h`

is `1`

if the test
rejects the null hypothesis at the 5% significance level, and `0`

otherwise.

returns
a test decision based on a `h`

= jbtest(`x`

,`alpha`

,`mctol`

)*p*-value computed using
a Monte Carlo simulation with a maximum Monte Carlo standard error less
than or equal to `mctol`

.

Jarque-Bera tests often use the chi-square distribution to estimate
critical values for large samples, deferring to the Lilliefors test
(see `lillietest`

) for small samples. `jbtest`

,
by contrast, uses a table of critical values computed using Monte
Carlo simulation for sample sizes less than 2000 and significance
levels from 0.001 to 0.50. Critical values for a test are computed
by interpolating into the table, using the analytic chi-square approximation
only when extrapolating for larger sample sizes.

[1] Jarque, C. M., and A. K. Bera. “A
Test for Normality of Observations and Regression Residuals.” *International
Statistical Review*. Vol. 55, No. 2, 1987, pp. 163–172.

[2] Deb, P., and M. Sefton. “The Distribution
of a Lagrange Multiplier Test of Normality.” *Economics
Letters*. Vol. 51, 1996, pp. 123–130. This paper
proposed a Monte Carlo simulation for determining the distribution
of the test statistic. The results of this function are based on an
independent Monte Carlo simulation, not the results in this paper.

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