This function performs the Jarque-Bera tests of normality either the robust or the classical way.

```
JarqueBeraTest(x, robust = TRUE, method = c("chisq", "mc"),
N = 0, na.rm = FALSE)
```

A list with class `htest`

containing the following components:

- statistic
the value of the test statistic.

- parameter
the degrees of freedom.

- p.value
the p-value of the test.

- method
type of test was performed.

- data.name
a character string giving the name of the data.

- x
a numeric vector of data values.

- robust
defines, whether the robust version should be used. Default is

`TRUE`

.- method
a character string out of

`chisq`

or`mc`

, specifying how the critical values should be obtained. Default is approximated by the chisq-distribution or empirically via Monte Carlo.- N
number of Monte Carlo simulations for the empirical critical values

- na.rm
defines if

`NAs`

should be omitted. Default is`FALSE`

.

W. Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth, Weiwen Miao

The test is based on a joint statistic using skewness and kurtosis
coefficients. The robust Jarque-Bera (RJB) version of utilizes
the robust standard deviation (namely the mean absolute deviation
from the median, as provided e. g. by `MeanAD(x, FUN=median)`

) to estimate sample kurtosis and skewness. For more details see Gel and Gastwirth (2006).

Setting `robust`

to `FALSE`

will perform the original Jarque-Bera test (see
Jarque, C. and Bera, A (1980)).

Gastwirth, J. L.(1982) *Statistical Properties of A Measure
of Tax Assessment Uniformity*, Journal of Statistical Planning
and Inference 6, 1-12.

Gel, Y. R. and Gastwirth, J. L. (2008) *A robust modification of
the Jarque-Bera test of normality*, Economics Letters 99, 30-32.

Jarque, C. and Bera, A. (1980) *Efficient tests for
normality, homoscedasticity and serial independence of regression
residuals*, Economics Letters 6, 255-259.

Alternative tests for normality as
`shapiro.test`

,
`AndersonDarlingTest`

, `CramerVonMisesTest`

, `LillieTest`

, `PearsonTest`

, `ShapiroFranciaTest`

`qqnorm`

, `qqline`

for producing a normal quantile-quantile plot

```
x <- rnorm(100) # null hypothesis
JarqueBeraTest(x)
x <- runif(100) # alternative hypothesis
JarqueBeraTest(x, robust=TRUE)
```

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