(Robust) Jarque-Bera Test for Assessing Normality From Skewness and Kurtosis

A goodness-of-fit test for normality based on sample skewness and kurtosis, in its classical form or the robust modification of Gel and Gastwirth (2008).

Usage

jarqueBeraTest(x, robust = TRUE, method = c("chisq", "mc"), R = 1000)

Arguments

x

a numeric vector of data values.

robust

logical, if TRUE (default) the robust test of Gel and Gastwirth (2008) is performed, otherwise the classical Jarque-Bera test.

method

a character string specifying how the p-value is computed, one of "chisq" (default, asymptotic chi-squared approximation) or "mc" (Monte Carlo simulation).

R

the number of Monte Carlo replicates used for method = "mc" (default is 1000).

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

parameter

the degrees of freedom (method = "chisq"), or the number of Monte Carlo replicates (method = "mc").

p.value

the p-value of the test.

method

a character string indicating the test performed and how the p-value was computed.

data.name

a character string giving the name of the data.

Details

This function performs either the classical Jarque-Bera test or the robust Jarque-Bera test proposed by Gel and Gastwirth (2008). The robust version (the default) replaces the classical standard deviation by the average absolute deviation from the median (MAAD), which makes the test considerably less sensitive to outliers. The kurtosis component is then scaled with the constant \(C_2 = 64\) derived in Gel and Gastwirth (2008), the skewness component with \(C_1 = 6\) as in the classical test.

With method = "chisq" the statistic is referred to its asymptotic chi-squared distribution with 2 degrees of freedom. With method = "mc" the p-value is estimated by Monte Carlo simulation from R samples of the same size drawn from the standard normal distribution, using the finite-sample correction \((m + 1)/(R + 1)\), where \(m\) is the number of simulated statistics at least as large as the observed one.

Missing values are silently removed.

Note

Based on code by W. Wallace Hui, Yulia R. Gel, Joseph L. Gastwirth and Weiwen Miao previously published as rjb.test() in the lawstat package, adapted to conform to package standards.

References

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.

See also

shapiro.test()

Other test.normality: andersonDarlingTest(), cramerVonMisesTest(), lillieTest(), pearsonTest(), shapiroFranciaTest()

Examples

set.seed(1)
x <- rnorm(100)

jarqueBeraTest(x)                   # robust version (default)
#> 
#> 	Robust Jarque-Bera test (chi-squared approximation)
#> 
#> data:  x
#> X-squared = 0.086947, df = 2, p-value = 0.9575
#> 
jarqueBeraTest(x, robust = FALSE)   # classical Jarque-Bera test
#> 
#> 	Jarque-Bera test (chi-squared approximation)
#> 
#> data:  x
#> X-squared = 0.087201, df = 2, p-value = 0.9573
#> 

# Monte Carlo p-value
jarqueBeraTest(x, method = "mc", R = 5000)
#> 
#> 	Robust Jarque-Bera test (Monte Carlo)
#> 
#> data:  x
#> X-squared = 0.086947, R = 5000, p-value = 0.9508
#> 

# heavy-tailed alternative
jarqueBeraTest(rt(100, df = 2))
#> 
#> 	Robust Jarque-Bera test (chi-squared approximation)
#> 
#> data:  rt(100, df = 2)
#> X-squared = 9299.2, df = 2, p-value < 2.2e-16
#>